Shaw - tom's webpage
SEX, AGE, HEIGHT, AND WEIGHT
Thomas R. Knapp
©
2012
PREFACE
Everybody is interested in sex, age, height, and weight. If all you know about a person is his(her) sex, age, height, and weight, you have a pretty good idea regarding what he(she) looks like [even without checking the Photographic Height/Weight Chart website.] Differences between males and females are discussed all of the time. (Vive la difference?!) Age is sometimes the only identifier in a news item. (Example: “57-year-old jumps from Golden Gate Bridge.”) Whole books have been written about height and weight, both collectively and separately. I can't think of any other variables that are both of general interest and have been studied so thoroughly. So what I have tried to do in this book is to share with you some of the information about sex, age, height, and weight that I have accumulated in the last 30 years or so. I hope you'll find it to be both enlightening and entertaining.
The first three chapters in what follows are devoted to sex (but not in the way that you’re thinking)--its measurement, the percentages of males and females in various populations, and a brief summary of the literature on sex differences. [The word “effect” appears in the title of Chapter 3 and some of the other chapters. It and the associated word “cause” will usually appear inside of quotation marks throughout this book. Sex, age, height, and weight are neither “manipulable” nor “randomly assignable”, so it is difficult if not impossible to determine whether or not they are “causes” of anything.]
The next seven chapters address age in most of its ramifications, including its measurement and the relationship between age and other variables.
Chapters 11-20 are devoted to height and weight--how to measure them, their frequency distributions in various populations, and lots of other things about those two variables.
The final chapter (21) is concerned with the “effect” of sex, age, height, and weight (in various combinations) on a number of interesting variables. That chapter includes some interesting real data for sex, age, height, and weight, plus one additional variable (cholesterol). Several analyses regarding those data are carried out and the results are summarized.
No special background is necessary for following the narrative. A modest familiarity with basic statistical concepts and a smattering of knowledge about research design and measurement should be sufficient.
I shall use the word SHAW as an acronym for sex, height, age, and weight. That’s not the right order, “covariately speaking”, since sex is more basic than age, which in turn is more basic than height, and weight is least basic, but SAHW is unpronouncible as are most of the other permutations of the letters S, A, H, and W. I also toyed with WASH, but that didn’t wash (bad pun), so SHAW it is. [I also am an admirer of the writings of George Bernard Shaw. If you haven’t yet read his marvelous essay, “The vice of gambling and the virtue of insurance”, please do so. You’ll have a real treat in store for yourself.]
TABLE OF CONTENTS
Chapter 1: THE MEASUREMENT OF SEX
Chapter 2: THE DISTRIBUTION OF SEX IN VARIOUS POPULATIONS
Chapter 3: THE “EFFECT” OF SEX
Chapter 4: THE MEASUREMENT OF AGE (FROM WOMB TO TOMB)
Chapter 5: THE USE OF COMPUTER PROGRAMS TO CALCULATE AGE
Chapter 6: THE DISTRIBUTION OF AGE IN VARIOUS POPULATIONS
Chapter 7: DIFFERENT KINDS OF AGES
Chapter 8: THE “EFFECT” OF AGE
Chapter 9: LIFE EXPECTANCY AS A FUNCTION OF AGE
Chapter 10: AGE ON OTHER WORLDS
Chapter 11: THE MEASUREMENT OF HEIGHT
Chapter 12: THE MEASUREMENT OF WEIGHT
Chapter 13: THE DISTRIBUTION OF HEIGHT IN VARIOUS POPULATIONS
Chapter 14: THE DISTRIBUTION OF WEIGHT IN VARIOUS POPULATIONS
Chapter 15: THE RELATIONSHIP BETWEEN HEIGHT AND WEIGHT
Chapter 16: ESTIMATING HEIGHTS AND WEIGHTS
Chapter 17: "IDEAL” WEIGHT
Chapter 18: BMI, BSA, BIA, and BMR
Chapter 19: THE “EFFECT” OF HEIGHT
Chapter 20: THE “EFFECT” OF WEIGHT
Chapter 21: THE COMBINED “EFFECT” OF VARIOUS SHAW SUBSETS
REFERENCES
CHAPTER 1: THE MEASUREMENT OF SEX
For most purposes there are only two ways to measure the sex of a person:
1. Ask the person to self-report whether he(she) is male or female; or
2. Look at the person and make the judgment.
The first of these is by far the more commonly employed, especially on questionnaires, which typically have two boxes labelled M and F, with the respondent asked to check one. But in some studies, e.g., quota-type surveys conducted in shopping malls or other public places, the investigator seeks out so many males and so many females by “eyeballing” who is which sex.
Babies at birth present an interesting sex measurement situation exemplified by the second method. The obstetrician, nurse, or midwife takes a look and proclaims “It’s a boy!” or “It’s a girl!”. [See the opening paragraph of the book by Diane Halpern (2000).] Sex can of course also be determined pre-natally by amniocentesis or ultrasound, whereby the mother herself can do the proclaiming.
Reliability and validity of the measurement of sex
But are these two methods reliable and valid? If a person reports himself (herself) as male (female) on a particular questionnaire on a given day, will he (she) also report himself (herself) as male (female) on a subsequent administration of that same questionnaire? Likewise for the eyeballer. And is the target person REALLY male (female)?
You may be tempted to say “Of course” to all of those questions. Why would a respondent not check the same box on both occasions? I can think of at least two reasons: (1) inattention (in hurrying through the questionnaire the person checks one of the boxes the first time and the other box the second time); and (2) orneriness (some people like to louse up researchers). How about the eyeballer? Again those same two reasons, plus a third one: The target person may have originally appeared to be of one sex but subsequently appeared to be of the opposite sex (perhaps due to a change of attire or hair style).
The preceding paragraph is concened with the reliability (consistency) of the measurement process. The “REALLY” question is one of validity. Would a female respondent check the male box (that’s a terrible pun) or a male respondent check the female box? Perhaps; and for the same reasons alluded to for unreliability, plus: if the time between the two administrations of the questionnaire is fairly long, an actual sex change may have occurred in the interim [unlikley, but possible]. And for the observational indication of sex there is the additional problem that things are occasionally not what they seem to be. Boys with long hair are often taken for girls, for example, and newborns’ genitalia are sometimes not perfectly differentiable.
Sex vs. “gender”
That leads naturally to one of the most confusing (to me, at least) problems in the “measurement” of sex, viz., what do we call the variable? Up until the last 50 years or so the word “sex” was always used to designate the male/female distinction. The word “gender” was strictly a grammatical term that identified nouns in various languages (not English) as masculine, feminine, or (for Latin) neuter according to their endings. It is now frequently the case that the word “gender” has replaced “sex” not only on questionnaires but also in popular discourse. There are allegedly important differences between the two words, as specified in the following quotation:
“Researchers should specify in publications their use of the terms sex and gender. To clarify usage and bring some consistency to the literature, the committee recommends the following:
• In the study of human subjects, the term sex should be used as a classification, generally as male or female, according to the reproductive organs and functions that derive from the chromosomal complement.
• In the study of human subjects, the term gender should be used to refer to a person’s self-representation as male or female, or how that person is responded to by social institutions on the basis of the individual’s gender presentation.
• In most studies of nonhuman animals the term sex should be used.”
(Institute of Medicine, 2001, Recommendation 7, page 8)
[Leonard Sax (2005), author of the book Why gender matters, and advocate of single-sex public education, doesn’t like the IOM’s recommendation. I don’t either, especially the definition of gender, which is circular. But I never use the term “gender” anyhow.]
You would not be aware of the sometimes subtle distinctions between the terms “sex” and “gender” by perusing much of the literature, however. I’ve seen books and articles devoted to studies of the differences between the sexes (genders?) in which approximately half of the citations are to sources with “sex differences” in their titles and the other half have “gender differences” in theirs. In her 1998 book, The two sexes, Eleanor Maccoby, one of the world’s leading authorities on the psychological differences between males and females, used the words sex and gender completely interchangeably. (For some other “takes” on sex vs. gender, see Halpern, 2000, Bullough, 2005, and the chapters by Poston and by Riley in the 2005 Handbook of population.) Interestingly, the internet encyclopedia Wikipedia has separate long articles on sex differences and gender differences, with the entry on sex differences having been “tagged” in July, 2007 for alleged inaccuracies.
CHAPTER 2: THE DISTRIBUTION OF SEX IN VARIOUS POPULATIONS
A note regarding the word “distribution”
When I use the word “distribution” in this chapter and throughout the rest of the book I am referring to the statistical frequency distribution of a variable and not to any of the other meanings of “distribution”.
The world (in the year 2000)
The exact figures are not known, since some countries don’t conduct censuses or don’t carry them out very well, but the UN estimated that there were approximately 3 billion males (50%) and aproximately 3 billion females (50%) in 2000, with males slightly outnumbering females (primarily because of the 1.02 male-to-female sex ratio at birth). [At the time of the writing of this paragraph in July, 2007 the best approximation, provided by the CIA in The World Factbook, 2003, was 3.32 billion males and 3.28 billion females.]
The United States as a whole (2000 census)
In the year 2000 there were approximately 138 million males (49.1%) and 143 million females (50.9%) [the actual numbers provided by the Census Bureau are 138,053,563 and 143,368,343, but some people are missed and others are double-counted, even in the most careful censuses]. The “sex breakdown” varies considerably with respect to age (that matter will be examined in Chapter 6) and other variables.
The United States as a whole (projection for the year 2050)
Males: 193,234,000 (49.1%)
Females: 200,696,000 (50.9%)
Same “breakdown” as 2000, at least to the nearest tenth of a percent. How dull.
(Source: U.S. Department of Commerce, 1996, Middle Series, Table 2, page 88)
Some other interesting populations
Males Females
United Arab Emirates (2000) 1,722,000 (66.1%) 884,000 (33.9%)
Licensed Drivers, Alaska (2000) 215,821 (46.4%) 249.435 (53.6%)
Nurses, U.S. 164,000 ( 6.5%) 2,343,000 (93.5%)
Police officers, U.S. 595,000 (88.4%) 78,000 (11.6%)
CHAPTER 3: THE “EFFECT” OF SEX
Certain differences between males and females are rather obvious, e.g., anatomical features, height and weight discrepancies, and the like, and such
differences will be given no more than a cursory mention in this chapter. But there is a vast literature regarding not-so-obvious differences, and it is to a brief summary of that literature to which I would now like to turn. The major emphasis will be on “big” differences, with passing references to “small” differences. The samples upon which the differences have been determined vary in both size and representativeness, so if you look up any of these sources please keep that in mind. Also keep in mind that certain claims regarding the presence or the absence of sex differences are politically controversial (see, for example, Eagly, 1995 and the comments regarding her article that appeared in a subsequent issue--February, 1996--of the American Psychologist).
Note 1: The discussion will be limited to differences between males and females as biologically identified. No attention will be given to “masculinity” and “femininity”. (See Maccoby, 1998 regarding various definitions of those terms---if you’re interested.) And although the terms “gender differences”, “sex-related differences”, and “gender-related differences” are used in the titles of some books and articles concerned with the differences between males and females, I will not use any of those terms. “Sex differences” will do just fine.
Note 2: If what follows strikes you as too extensive and/or too complicated, just read the dictionary of sex differences with the delightful title, Why Eve doesn’t have an Adam’s apple, by Carol Ann Rinzler, and you’ll get the picture. That book is a little outdated (1996) and was apparently written primarily for young adults (the copy that I borrowed from our local library has a YP before the Dewey Decimal System 612.6 designation). If you find that too “babyish” (which I doubt), go on to read science writer Robert Pool’s 1994 book with the equally intriguing title, Eve’s rib. He writes extremely well about sex differences and the studies upon which claims regarding such differences have been made. [There are at least three books with the title, Eve’s rib; the other two that I know of are by Nowak(1980) and by Legato (2002). All deal with sex differences.]
Big differences
What is a “big” difference? It is a difference that (a) leaps out at you; and/or (b) equals eight-tenths or more of a standard deviation [Cohen’s (1988) “large” effect size]; and/or (c) is statistically significant yet not based upon a huge sample size for which statistical significance, but not necessarily practical significance, is almost guaranteed. Here are some of those differences:
Jumping from Golden Gate Bridge: In my Preface I gave jumping from that bridge as a hypothetical example of a news headline. There recently (August 1, 2007) appeared the following headline in USA TODAY: “Most Golden Gate jumpers are local”. The writer (John Ritter) goes on to say that of 203 people confirmed to have jumped in the ten-year period from July, 1997 to July, 2007, males outnumbered females by approximately 3 to 1 (i.e., 75% of the jumpers were males). [Please forgive me for starting with this one. I just found it to be extremely interesting.]
Users of the filler word “like”: Three teenagers at a Scarsdale, NY high school (Thomas Levine, Andrea Nehorayoff, & Ariel Millhauser, 2007) studied the use of that annoying (to many people) word by males and females at their school. They found that it was used statistically significantly more often by females than by males. [I also found this study to be extremely interesting, and particularly impressive in that it was apparently carried out by those three students under the guidance of, but with little or no other assistance by, their teachers.]
The senses: Females generally have much greater acuity in hearing (see Corso, 1959; 1963). There is some evidence that males have slightly better visual acuity (McGuinness, 1976). See also the section on perceptual and motor skills in Halpern (2000).
Finger lengths: The ring fingers of males are usually longer than their index fingers, whereas those two fingers are of approximately equal length for females. There is some evidence that the ratio of ring finger length to index finger length is predictive (but of course not necessarily causally) of several variables, including academic ability and aggression! (See Manning, 2002 and Eachus, 2007.)
Health: In the long chapter entitled “Sex affects health”, the contributors to the Institute of Medicine’s book on sex differences point out that males and females have different patterns of illnesses, and all are not necessarily attributable simply to their “maleness” or “femaleness”. For example, the prevalence of obesity is greater for females than for males, especially for certain ethnic groups (see their Table 5-4). And males and females differ considerably in their reactions to drugs and to drug dosages.
Pain: Females are more sensitive than males to pain, but seek more help to alleviate it and derive more relief from such help. (See, for example, Berkley, 1997a,b; Unruh, 1996; Unruh, Ritchie, & Merskey, 1999.)
Automobile accidents: Males are much more likely to be involved than females, with males constituting about 73% of all traffic fatalities. See Evans (2006) for this and much more regarding sex differences in driving behavior.
Infant mortality: Greater for males. In the United States the male-to-female sex ratio at birth of approximately 1.05 drops considerably to almost 1.0 by one year of age because of that, and stays fairly close to 1.0 until about age 65, where it becomes about .70, i.e., there are many more females than males in the older age groups. See, for example, The (CIA’s) World Factbook, 2003.
Life expectancy: Consistently higher for women, by approximately five or six years. Some claim that the difference has been largely attributable to the difference in smoking prevalence for the two sexes (see, for example, Gorman & Read, 2007 and the references cited therein), and, if so, the difference in life expectancy should narrow as the percentages of both male smokers and female smokers get smaller and closer together.
Mathematical ability: The seminal work was carried out by Benbow and Stanley (1980) and reported in a brief three-page article in the prestigious journal, Science. In their study of 9927 gifted junior high school students they found that the boys scored considerably higher than the girls on the quantitative section of the Scholastic Aptitude Test (SAT), which was and still is intended for high school students. Their findings caused an uproar in the research community, mainly by advocates of the nurture side of the nature vs. nurture controversy (see, for example, Schafer & Gray, 1981), but Benbow and Stanley held their ground (see Benbow & Stanley, 1981, 1983; and Benbow, 1988 for their rejoinders). [As Pool (1994) points out, there is a surprisingly small difference between males and females on the verbal section of the SAT, however. See Hyde & Linn, 1988 for a meta-analysis on that topic.]
Intelligence: As you can imagine, whether or not females are smarter than males or males are smarter than females is even more controversial than the reported findings of sex differences in mathematics. Two of the best sources for empirical evidence regarding sex differences in intelligence are Feingold (1988) and Halpern (1989, 1997, 2000)--see also Bennett (1996, 1997) for differences in how males and females estimate their own abilities. A complicating factor is that some psychologists claim there are different “intelligences”, with respect to which males excel on some (e.g., spatial visualization--see Sanders, Soares, & D’Aquila, 1982 and Masters & Sanders, 1993) and females excel on others (e.g., memory--see McGuiness, Olson, & Chapman, 1990). But this is what one psychologist had to say: “Are men smarter than women? The answer to the above burning question is: No, they are not. Data are now being laid on the table that show that, on average, men and women are equal in mental ability.”
[Seligman, 1998, p. 72, cited in Halpern, 2000, p. 81.]
Income, adults age 15+: Huge difference in favor of males in general (see, for example, Figure 3, page 11 in DeNavas-Walt, Proctor, & Lee, 2006), and for male psychiatrists in particular (see Weeks & Wallace, 2007), although the gap in earnings between males and females in most occupations and professions seems to be narrowing, if one takes into account welfare [in the general economic sense, not in the governmental-dependent sense] as well as income (see Murphy, 2003).
So what?
Males and females differ in lots of respects. Is there anything we can do about it? Do we want to do anything about it? The answer to the first question is: Sometimes. The answer to the second question is: Yes, if that would help to minimize sex discrimination.
Some of the things we can’t and/or don’t want to do anything about are jumping off Golden Gate Bridge and finger length. Some of the things that we can and should do something about are differences in the use of “like” as a filler word and income. For most of those differences the best strategy is not to reverse the direction of the difference (nobody wants to make males use “like” more often than females do, for example) but to try to put in place some educational interventions that might help to equalize the sexes (better training in spatial visualization for females? sensitivity training for personnel decision-makers regarding salaries for females and males who perform the same jobs?) Most sex differences are likely to be with us for a long time, however.
CHAPTER 4: THE MEASUREMENT OF AGE (FROM WOMB TO TOMB)
Gestational age
Let’s start at the very beginning. How do we measure the age of a newborn, i.e., gestational age? There are actually three or four competing approaches to that problem:
1. Subtract date of conception from date of birth.
2. Subtract date of last menstrual period from date of birth.
3. Use the Dubowitz/Ballard scale.
4. [Not recommended, by me anyhow.] Use clinical observation and experience, without incorporating any sort of scale or calculation.
It goes without saying that date of conception is very difficult to determine (how can we know?) but date of last menstrual period is easily approximated since most women are very conscious of the timing of their menstrual periods.
The Dubowitz/Ballard scale was originally two different scales, one due to Dubowitz and the other due to Ballard, but they have been combined into one:
• The Dubowitz/Ballard Examination evaluates a baby's appearance, skin texture, motor function, and reflexes. The physical maturity part of the examination is done in the first two hours of birth. The neuromuscular maturity examination is completed within 24 hours after delivery.
• Physical maturity:
The physical assessment part of the Dubowitz/Ballard Examination looks at physical characteristics that look different at different stages of a baby's gestational maturity. Babies who are physically mature usually have higher scores than premature babies.
Points are given for each area of assessment, with a low of -1 or -2 for extreme immaturity to as much as 4 or 5 for postmaturity. Areas of assessment include the following:
o skin textures (i.e., sticky, smooth, peeling).
o lanugo (the soft downy hair on a baby's body) - is absent in immature babies, then appears with maturity, and then disappears again with postmaturity.
o plantar creases - these creases on the soles of the feet range from absent to covering the entire foot, depending on the maturity.
o breast - the thickness and size of breast tissue and areola (the darkened ring around each nipple) are assessed.
o eyes and ears - eyes fused or open and amount of cartilage and stiffness of the ear tissue.
o genitals, male - presence of testes and appearance of scrotum, from smooth to wrinkled.
o genitals, female - appearance and size of the clitoris and the labia.
• Neuromuscular maturity:
Six evaluations of the baby's neuromuscular system are performed. These include:
o posture - how does the baby hold his/her arms and legs.
o square window - how far the baby's hands can be flexed toward the wrist.
o arm recoil - how far the baby's arms "spring back" to a flexed position.
o popliteal angle - how far the baby's knees extend.
o scarf sign - how far the elbows can be moved across the baby's chest.
o heel to ear - how close the baby's feet can be moved to the ears.
A score is assigned to each assessment area. Typically, the more neurologically mature the baby, the higher the score.
When the physical assessment score and the neuromuscular score are added together, the gestational age can be estimated. Scores range from very low for immature babies (less than 26 to 28 weeks) to very high scores for mature and postmature babies.
[Source: University of Virginia Health System website]
Traditional chronological age
After birth has taken place the usual way to measure age is to subtract date of birth from date at which age is to be determined. That sounds straightforward enough, but it can be a bit tricky, primarily because three variables are involved (month, day, and year) and things can get complicated. For example, how old on June 6th, 2008 would a person be who was born on September 19th, 1969? Setting it up like a typical subtraction problem we have:
Month Day Year
6 6 2008
- 9 19 1969
Hmmm. We can’t subtract 9 from 6 or 19 from 6, but we can subtract 1969 from 2008. In order to do the Year subtraction, however, we must first convert the Month and the Day for the later year (2008) to the 17th month and the 36th day of 2007. (June 6th, 2008 is the sixth day of what would be the 18th month of 2007, but it would be the 37th day of the fifth month--May--of 2007.) That gives us:
Month Day Year
17 37 2007
- 9 19 1969
Carrying out the subtraction, this person would be 38 years, 8 months, and 18 days old on June 6th, 2008. One might want to round this down to 38 (years of life completed) or round up to 39 (since the person is closer to 39 years of age than to 38).
Age of skeletons
If death has taken place, and the age of the decedent is unknown, age at death can be estimated by the use of various forensic methods. Samworth and Gowland (2005) have summarized some of those methods and the statistical assumptions upon which they are based. Most methods involve skull or teeth measurements, or, occasionally, both. A fascinating example of forensic identification is "Earl", a skeleton whose sex, age, height, and weight were estimated by Terrie Winson (Kutztown University, PA). See her website for all of the details; its address is forensics. And see Chapter 16 for forensic estimation of the heights and weights of corpses.
CHAPTER 5: THE USE OF COMPUTER PROGRAMS TO CALCULATE AGE
In the previous chapter I referred to the traditional measurement of age by subtracting date of birth from current date (rounding down or up, as desired). That calculation is a rather difficult arithmetical exercise, as illustrated by the example in that chapter. Fortunately, computers (actually computer algorithms) have come to our rescue. There are five readily-available routines for calculating one’s age. In order of my preference (from most to least), they are:
1. The marvelous Age Calculation Machine (Athens/Troy/8697/agecalculator.html), whereby you enter only your date of birth (to the nearest year, month, day, hour, minute--however accurately you know it) and it returns your age as of the current date (it knows what that is) to the nearest millisecond (!) right before your eyes, as well as the time to your next birthday. Amazing.
2. Pete Russell’s “Your Age in Days” webpage (age.html). Input date of birth; output age in days.
3. The AGS Publishing Age Calculator (). Input date of birth, output age in years, months, and days.
4. The SAS command age = INT ( (today( ) - db) / 365.25 )
where today() is the function that calculates the number of days between October 15th,1582 and the current date; db is the person's date of birth; and INT is the function that subtracts the integer part of the result from the number of years.
5. The SPSS command age = TRUNC ( ( $jdate - yrmoda(xdate.year(db) , xdate.month(db) , xdate.mday(db) ) ) / 365.25 )
where $jdate is the system variable that returns the number of days between that same date of October 15th, 1582 and the current date, using the Gregorian Calendar; xdate.year, xdate.month, xdate.mday are functions that extract year, month, day from db (date of birth); yrmoda is the function that calculates the number of days between October 15th,1582 and the date of birth; and trunc is the function that extracts years minus the integer part of the result.
CHAPTER 6: THE DISTRIBUTION OF AGE IN VARIOUS POPULATIONS
The U.S. in the year 2000
In the table that follows I have reproduced from the CensusScope website the distribution of age, by sex, in the United States in the year 2000. Here are the numbers and the corresponding percentages).
|Age Distribution by Sex, 2000 |
| |Male | |Female | |
| |Number | % |Number | % |
|Total Pop. |138,053,563 |49.06 |143,368,343 |50.94 |
|0-4 |9,810,733 |3.49 |9,365,065 |3.33 |
|5-9 |10,523,277 |3.74 |10,026,228 |3.56 |
|10-14 |10,520,197 |3.74 |10,007,875 |3.56 |
|15-19 |10,391,004 |3.69 |9,828,886 |3.49 |
|20-24 |9,687,814 |3.44 |9,276,187 |3.30 |
|25-29 |9,798,760 |3.48 |9,582,576 |3.41 |
|30-34 |10,321,769 |3.67 |10,188,619 |3.62 |
|35-39 |11,318,696 |4.02 |11,387,968 |4.05 |
|40-44 |11,129,102 |3.95 |11,312,761 |4.02 |
|45-49 |9,889,506 |3.51 |10,202,898 |3.63 |
|50-54 |8,607,724 |3.06 |8,977,824 |3.19 |
|55-59 |6,508,729 |2.31 |6,960,508 |2.47 |
|60-64 |5,136,627 |1.83 |5,668,820 |2.01 |
|65-69 |4,400,362 |1.56 |5,133,183 |1.82 |
|70-74 |3,902,912 |1.39 |4,954,529 |1.76 |
|75-79 |3,044,456 |1.08 |4,371,357 |1.55 |
|80-84 |1,834,897 |0.65 |3,110,470 |1.11 |
|85+ |1,226,998 |0.44 |3,012,589 |1.07 |
As you can see, there were more men than women under age 34, due primarily to the well-known phenomenon that in any given year there are more male births than there are female births. But thereafter there were more women than men, and the difference was greatest at the older ages, with almost three times as many women as men in the 85+ age group.
Two unusual distributions
But those data are for the population of the entire country. Here are the age distributions for two places with quite different populations for that same year (the first is for Grant County, North Dakota; the second is for Orange County, Florida):
|Age Distribution by Sex, 2000 Grant County |
| |Male | |Female | |
| |Number |Percent |Number |Percent |
|Total Population |1,449 |51.00% |1,392 |49.00% |
|0-4 |63 |2.22% |60 |2.11% |
|5-9 |84 |2.96% |74 |2.60% |
|10-14 |116 |4.08% |96 |3.38% |
|15-19 |127 |4.47% |99 |3.48% |
|20-24 |42 |1.48% |26 |0.92% |
|25-29 |52 |1.83% |51 |1.80% |
|30-34 |77 |2.71% |44 |1.55% |
|35-39 |74 |2.60% |77 |2.71% |
|40-44 |103 |3.63% |103 |3.63% |
|45-49 |110 |3.87% |111 |3.91% |
|50-54 |108 |3.80% |97 |3.41% |
|55-59 |97 |3.41% |82 |2.89% |
|60-64 |87 |3.06% |78 |2.75% |
|65-69 |81 |2.85% |76 |2.68% |
|70-74 |80 |2.82% |92 |3.24% |
|75-79 |62 |2.18% |74 |2.60% |
|80-84 |45 |1.58% |58 |2.04% |
|85+ |41 |1.44% |94 |3.31% |
|Age Distribution by Sex, 2000 Orange County |
| |Male | |Female | |
| |Number |Percent |Number |Percent |
|Total Population |443,716 |49.50% |452,628 |50.50% |
|0-4 |31,444 |3.51% |29,931 |3.34% |
|5-9 |33,477 |3.73% |31,764 |3.54% |
|10-14 |32,690 |3.65% |30,982 |3.46% |
|15-19 |32,108 |3.58% |31,234 |3.48% |
|20-24 |35,810 |4.00% |34,953 |3.90% |
|25-29 |37,543 |4.19% |36,375 |4.06% |
|30-34 |38,798 |4.33% |36,339 |4.05% |
|35-39 |40,870 |4.56% |39,405 |4.40% |
|40-44 |36,869 |4.11% |36,477 |4.07% |
|45-49 |30,169 |3.37% |31,048 |3.46% |
|50-54 |25,010 |2.79% |26,286 |2.93% |
|55-59 |17,982 |2.01% |19,431 |2.17% |
|60-64 |13,757 |1.53% |15,633 |1.74% |
|65-69 |12,022 |1.34% |14,042 |1.57% |
|70-74 |10,063 |1.12% |13,242 |1.48% |
|75-79 |7,616 |0.85% |11,194 |1.25% |
|80-84 |4,663 |0.52% |7,474 |0.83% |
|85+ |2,825 |0.32% |6,818 |0.76% |
As you can see, the Grant County distribution has proportionally more people in the 85+ age group than for the entire country, whereas the Orange County distribution has proportionally more in the younger age groups. [Although the state of Florida as a whole has a fairly high concentration of retirees, such is not the case for Orange County.]
The distribution of age at death of presidents of the United States
Consider the following raw data regarding age at death of the various presidents of the United States, in chronological order according to date of death and "rounded down" to completed years of life:
|NAME | | |AGE | |
|Washington, George | | |67 | |
|Jefferson, Thomas | | |83 | |
|Adams, John | | |90 | |
|Monroe, James | | |85 | |
|Madison, James | | |72 | |
|Harrison, William H. | | |68 | |
|Jackson, Andrew | | |78 | |
|Adams, John Q. | | |74 | |
|Polk, James K. | | |53 | |
|Taylor, Zachary | | |65 | |
|Tyler, John | | |71 | |
|Van Buren, Martin | | |79 | |
|Lincoln, Abraham | | |56 | |
|Buchanan, James | | |77 | |
|Pierce, Franklin | | |64 | |
|Fillmore, Millard | | |74 | |
|Johnson, Andrew | | |66 | |
|Garfield, James A. | | |49 | |
|Grant, Ulysses S. | | |63 | |
|Arthur, Chester A. | | |56 | |
|Hayes, Rutherford B. | | |70 | |
|Harrison, Benjamin | | |67 | |
|McKinley, William | | |58 | |
|Cleveland, Grover | | |71 | |
|Roosevelt, Theodore | | |60 | |
|Harding, Warren G. | | |57 | |
|Wilson, Woodrow | | |67 | |
|Taft, William H. | | |72 | |
|Coolidge, Calvin | | |60 | |
|Roosevelt, Franklin | | |63 | |
|Kennedy, John F. | | |46 | |
|Hoover, Herbert | | |90 | |
|Eisenhower, Dwight | | |78 | |
|Truman, Harry S | | |88 | |
|Johnson, Lyndon B. | | |64 | |
|Nixon, Richard M. | | |81 | |
|Reagan, Ronald | | |93 | |
|Ford, Gerald | | |93 | |
| | | | | |
|Carter, James E.* | | | | |
|Bush, George H.W.* | | | | |
|Clinton, William J.* | | | | |
|Bush, George W.* | | | | |
• Carter, George H.W. Bush, Clinton, and George W. Bush (the current president) are still alive (as of the writing of this chapter).
Here is one possible frequency distribution for those ages (you get a different one every time you choose different age intervals):
Age Tally Frequency
45-49 11 2
50-54 1 1
55-59 1111 4
60-64 111111 6
65-69 111111 6
70-74 1111111 7
75-79 1111 4
80-84 11 2
85-89 11 2
90-94 111 4
The majority of the presidents died in their sixties or seventies. The median age at death was 69.
Heaping
All of the preceding age distributions were "grouped" frequency distributions, with ages divided into various intervals such as 0-4, 5-9, 10-14, etc. Something very interesting happens for distributions by single years of age, i.e., "ungrouped" distributions, when ages are self-reported. You usually get "heaping" at ages that end in 0 and 5. That is because people have a tendency to round freely to ages such as 30, 35, 40, etc. For example, some of those who are 29 years of age are likely to call themselves 30 rather than 29; likewise for those who are 31.
Demographers and census-takers are frustrated by the somewhat strange distributions they obtain for single years of age. It is in this context that the term "heaping" was first coined (by Shryock & Siegel, 1971). As is the case with weights, there is heaping at years of age ending in 0 and 5, with unusually low frequencies in between. [There are tests for the degree of heaping in a frequency distribution. See, for example, Roberts & Brewer, 2001.]
An interesting example of "double heaping" (heaping at certain ages on both of two variables that are being correlated with one another) has been provided by Maltz (1998) in his research on the relationship between age of offender and age of victim in homicides. He found that police officers had a tendency to not only round their estimates to ages ending in 0 or 5 but also to equate the age of the victim to the age of the offender in the absence of any information to the contrary.
In his article entitled "The great enumeration", Gerald Carson (1979) claimed that in the 1940 U.S. census there was considerable heaping at the age of 65, because of the recently-passed Social Security legislation stipulating that only those of age 65 and over were eligible. The data recently summarized by the Bureau of the Census in its Current Population Reports do not support that claim, however. Here are some population estimates for 1939, 1940, and 1941:
Year 1939 Year 1940 Year 1941
Age 64 860846 877311 899735
Age 65 822091 838519 858629
Age 66 781324 801110 819065
There were fewer people who called themselves 65 in 1940 than called themselves 64 one year earlier, most likely attributable to the usual situation of more deaths at the older age. The data for ages 64, 65, and 66 in 1940 do also not support a heaping hypothesis, since the numbers on each side of the 838519 are not both lower than 838519. [Perhaps the original data have been "smoothed" to adjust for heaping before they were published in the source cited. That is a commonly-employed practice by demographers, epidemiologists, and statisticians.]
CHAPTER 7: DIFFERENT KINDS OF AGES
Dorland’s Medical Dictionary (see MerckSource website) defines chronological age as “the duration of individual existence measured in units of time”, but goes on to list 15 attributes relative to chronological age. They are:
achievement age, a measure of achievement expressed in terms of the chronological age of an average child showing the same degree of attainment.
anatomical age, age expressed in terms of the chronological age of the average individual showing the same body development.
Binet age, mental age as determined by Binet's test.
bone age, osseous development shown radiographically, stated in terms of the chronological age at which the development is ordinarily attained.
chronological age, the age of a person expressed in terms of the period elapsed from the time of birth.
coital age, the age of a conceptus defined by the time elapsed since the coitus that led to fertilization.
developmental age, age estimated from the degree of anatomical development. In psychology, the age of an individual as determined by the degree of his emotional, mental, anatomical, and physiologic maturation.
emotional age, the age of an individual expressed in terms of the chronological age of an average normal individual showing the same degree of emotional maturity.
fertilization age, conceptus age defined by the time elapsed since fertilization.
functional age, the combined expression of the chronological, emotional, mental, and physiological ages of an individual.
gestational age, age of conceptus or pregnancy. In human clinical practice, pregnancy is timed from onset of the last normal menstruation. Elsewhere the onset may be timed from estrus, coitus, artificial insemination, vaginal plug formation, fertilization, or implantation.
menstrual age, conceptus age defined by the time elapsed since the onset of the mother's last normal menstruation.
mental age, the score achieved by a person in an intelligence test, expressed in terms of the chronological age of an average normal individual showing the same degree of attainment.
physical age, physiological age, the age of an individual expressed in terms of the chronological age of a normal individual showing the same degree of anatomical and physiological development.
postovulatory age, conceptus age defined by the time elapsed since release of the oocyte from the ovary.
I have already discussed one of them: gestational age. In this chapter I would like to concentrate on two of the others in that list of 15 (developmental age, mental age), along with three others that are of particular interest to me (age of reason, drinking age, smoking age). [There are even more kinds, e.g., advanced paternal age (age of a man who is greater than or equal to 40 years of age at time of conception); and coronary age (see Schisterman & Whitcomb, 2004); but let's not get carried away!]
The concept of developmental age was originally based upon the work of Gesell and the norms for the Gesell School Readiness Test (Ilg & Ames, 1965). More recently, there has been supporting evidence for the usefulness of that test for the prediction of school success (see, for example, Wood, Powell, & Knight, 1984). There has also been some associated research regarding the ability of mothers to estimate the developmental ages of their preschool children (Pulsifer, Palmer, & Capute, 1994; Glascoe & Sandler, 1995). Developmental quotients (developmental age divided by chronological age, multiplied by 100) have been found to be useful for surveillance of developmental disabilities (Pulsifer, Palmer, & Capute, 1994).
The concept of mental age has a similar and even longer history, dating back to the work of Binet just after the turn of the 20th century. His first tests of intelligence awarded months of mental age to the successful completion of various mental tasks, and, just as for developmental age, an intelligence quotient (mental age divided by chronological age, multiplied by 100--the well-known IQ score) was calculated. That calculation has since been replaced by the determination of a “deviation IQ”, where a person’s IQ score is a function of the person’s relative position in a frequency distribution of intelligence test scores obtained by persons of the same chronological age.
Age of reason is a concept that is crucial in the Roman Catholic Church. A person is said to have reached the age of reason (usually age 7) when (s)he is capable of distinguishing between right and wrong, and therefore guilty of sinning if (s)he chooses to do wrong. [There is also a book entitled The age of unreason, by Charles Handy, but it is concerned with discontinuous change in modern capitalism, not with the years before age 7. Historians are always talking about "The age of" with respect to various time periods. That special notion of age is not considered any further in this book.]
Smoking age is the minimum age at which a person can legally purchase tobacco products (usually cigarettes). Each state establishes its own minimum age, and as of the writing of this book that age is 18 for 47 of the 50 states and 19 for Alabama, Alaska, and Utah.
Drinking age is the minimum age at which a person can legally purchase alcoholic beverages. That age is also established by each state, and as of the writing of this book it is 21 for all 50 states (with several interesting exceptions--see the Alcohol: Problems and Solutions website).
Are those ages (smoking age and drinking age) too high? Too low? Just right? That’s a very difficult matter--morally, politically, and economically. There has been at least one attempt to estimate the cost effectiveness of raising the minimum smoking age (Ahmad, 2005). And sociologist David Hanson [who maintains the Alcohol: Problems and Solutions website] claims that the setting of the minimum drinking age is based on ideology and not on science.
CHAPTER 8: THE “EFFECT” OF AGE
Age is usually an independent variable in most research, i.e., the researcher is most likely to be interested in the "effect" (not necessarily in the causal sense of that word) of age on other variables such as reading achievement, happiness, mortality, etc. The purpose is to assess the extent to which a person's "score" on those variables are predictable from his(her) age. As expected, there is a rather strong positive correlation between age and reading achievement at the early ages, but little or no correlation in adulthood; an even stronger correlation between age and mortality; and very little correlation between age and happiness.
An interesting example is the chart review study of the “effect” of age on breast cancer care of 374 patients (Greenfield, Blanco, et al., 1987). Patients 50-69 years of age were found to receive better care than patients 70 years of age or older (96% of the former group received appropriate surgery, as compared to 83% for the latter group).
Another example is the research by Chu (1994) regarding age differences in driving habits of the elderly. She found that relative to persons aged 25-64 the elderly (age 65+) drive less in general; avoid driving at night, during peak hours, and on limited-access highways; and drive at lower speeds, using larger automobiles, and carrying fewer passengers.
Ray C. Fair has written two fascinating papers on “age effects”, one regarding baseball (2005), the other regarding athletic performance in general and competence in chess (2007). For baseball, performance gets better with age initially and then gets worse as age increases, particularly for pitchers. For some other sports the decline after age 35 or thereabouts starts out gradually and then gets much steeper. For chess the decline is not nearly as steep. [The mathematics in the two papers by Fair is a bit heavy at times, but just read around it and you’ll enjoy what you read. At least I did!]
As people get older their blood pressure tends to increase: systolic (the “top number”), goes up, and diastolic (the “bottom number”), goes down. [See the entry for High Blood Pressure, and the accompanying references, on the website.]
Age cohorts
Much of the age literature is concerned with various "cohorts", i.e., groups of people who share a particular demographic event, usually year of birth. The most studied cohort is the so-called "baby boom cohort", those people who were born during the period from 1946 to 1964. And in a recent study, DeVaney and Chiremba (2005) compared the retirement savings behavior of four cohorts:
1. The "swing" cohort [mine] (1928-1945)
2. The older baby boomers (1946-1954)
3. The younger baby boomers (1955-1964)
4. The "generations X and Y" cohort (1965-1987)
They found that the older baby boomers were most likely to hold a retirement account, but the "swing" cohort had the greatest amount of savings.
Age in years vs. year of birth
If you calculate the correlation between age in years and variables such as height and weight, the correlation is positive; i.e., as age increases, height and weight generally also increase (at least for the younger ages). But if you carry out those same calculations using year of birth rather than age in years the correlation is negative; i..e., as year of birth increases (e.g., from 2000 to 2007) both height and weight generally decrease, since the higher (more recent) birth years correspond to younger years of age. The constructs (age and height, age and weight) are positively correlated but the correlation coefficient can be a negative number as an artifact of the way in which age is measured.
Variability
What happens as we grow older? Do we tend to be more like one another or less like one another than we were at earlier ages? Those questions have received a great deal of attention. It was originally argued that variability increased with age, especially in cognitive ability (see, for example, Kermis, 1984), but later research (e.g., Morse, 1993) refuted that claim.
In a series of two articles and a book, the well-known expert in gerontology, E.B. Palmore (1977, 1981, 1998), presented a variety of forms of a test called the Facts on Aging Quiz (FAQ--an abbreviation not to be confused with that for Frequently Asked Questions). That quiz attempts to assess people's knowledge concerning what happens as we grow older. There are many misconceptions, e.g., that at least a tenth of older adults are in nursing homes (it's closer to 5% for people over age 65) and that most people become more religious as they age (those senior citizens who are religious now were religious when they were younger; it remains to be seen what will happen to younger adults when they get older). Palmore also refers to the earlier aging literature that claims people get more different from one another as they grow older.
CHAPTER 9: LIFE EXPECTANCY AS A FUNCTION OF AGE
Life expectancy is a concept that is concerned with the mortality experience of a hypothetical group of infants born at the same time and subject throughout their lifetime to the specific mortality risks of a given year. In the United States in the year 2000 life expectancy at birth was 76.9 years. (It is different between males and females: females tend to live longer; and it varies from race to race: Whites tend to live longer than Blacks.) The following table consists of some data excerpted from a life expectancy table for the United States for that year that are of particular interest to me: e x (expectation of life at age x) and q x (probability of dying between age x and age x+1) for the total population, averaged across both sexes and both races.
Age (x) e x q x
0 76.9 .006930
10 67.6 .000125
20 57.8 .000945
30 48.3 .001050
40 38.9 .002021
50 30.0 .004443
60 21.6 .010446
70 14.4 .024673
80 8.6 .058841
90 4.7 .148322
100+ 2.6 1.00000
Source: Arias (2002)
Let us take myself as an example. At the time of the writing of this book I am 77 years old. Using rough interpolation, my remaining life expectancy is a little over 10 years, and the probability that I will die before I reach age 78 is approximately .04. I of course might get hit by a truck and die tomorrow; I might live well beyond 87+; or anything in between.
There are a few fascinating features about this table. First of all, the probability of dying between age 0 and age 1 is almost 69 times the probability of dying between age 10 and age 11. That is because of the dangers to survival in the first year of life. Secondly, the life expectancy at age 100+ is greater than 0 but the probability of living for another year (= 1 - the probability of dying) is equal to 0! Finally, the first two columns add up to numbers that are increasingly greater than 76.9 at every age. That is because once you survive to an age greater than 0 you have a longer life expectancy. [Got that?]
There is also a clever calculator available on the internet (calculator) that estimates the likelihood of a person's living to age 100, based upon that person's answers to various questions. Try it. You may like it (or not,depending upon your result and whether or not you want to live that long!).
Another calculator (at ) estimates life expectancy based upon answers to 15 specific questions.
Life expectancy of animals
People have even worked out the life expectancy for various breeds of dogs and cats. It is fairly well known that small dogs live longer than large dogs (on the average). Here is an excerpt from a more detailed discussion of life expectancies for dogs and cats:
"People most commonly ask about how long they can expect to have their dog or cat. The concern and fear of losing a much-loved pet usually motivate the question. Cats on average live to their early teens. Exceptions are common. I once treated an eighteen-year old cat called Tiger. He required eye surgery. Routine blood work revealed a metabolic disease, which was easily treated. Six months after he was well, the family dog accidentally stepped on Tiger breaking a leg too severely to attempt treatment. Who knows how long Tiger might have survived? I have treated cats at twenty-four years of age.
Dogs tend to follow the old adage "The bigger they are, the harder they fall." Great Danes and other giant breeds rarely live beyond seven to nine years. Rottweilers and other heavy breeds usually live only into the early teens. Little mixed breeds often survive into their late teens. All of this of course depends on good health, which in turn is related to diet, exercise and general care. Veterinarians recommend regular blood screens for early detection of disease in geriatric animals. Like people with good genetics, there are variations within breeds with some lines of animals being particularly long-lived.
I don't know all of the reasons people ask this question of their veterinarian so often, but as a pet owner I have always envied people with very elderly animals. I have lost two beloved pets to cancer at relatively early ages. It is important to remember the quality of a pet's life as well as length, and preserve that quality though excellent preventative health care, making necessary changes in an animal's exercise and diet as they age."
[Source: The Pet Professor's website.]
Now for some estimates of the life expectancies of various breeds of dogs:
|Afghan Hound (12.0) |Greyhound (13.2) |
|Airedale Terrier (11.2) |Irish Red and White Setter (12.9) |
|Basset Hound (12.8) |Irish Setter (11.8) |
|Beagle (13.3) |Irish Wolfhound (6.2) |
|Bearded Collie (12.3) |Jack Russell Terrier (13.6) |
|Bedlington Terrier (14.3) |Labrador Retriever (12.6) |
|Bernese Mountain Dog (7.0) |Lurcher (12.6) |
|Border Collie (13.0) |Miniature Dachshund (14.4) |
|Border Terrier (13.8) |Miniature Poodle (14.8) |
|Boxer (10.4) |Norfolk Terrier (10.0) |
|Bull Terrier (12.9) |Old English Sheepdog (11.8) |
|Bulldog (6.7) |Pekingese (13.3) |
|Bullmastiff (8.6) |Random-bred / Mongrel (13.2) |
|Cairn Terrier (13.2) |Rhodesian Ridgeback (9.1) |
|Cavalier King Charles Spaniel (10.7) |Rottweiler (9.8) |
|Chihuahua (13.0) |Rough Collie (12.2) |
|Chow Chow (13.5) |Samoyed (11.0) |
|Cocker Spaniel (12.5) |Scottish Deerhound (9.5) |
|Corgi (11.3) |Scottish Terrier (12.0) |
|Dachshund (12.2) |Shetland Sheepdog (13.3) |
|Dalmatian (13.0) |Shih Tzu (13.4) |
|Doberman Pinscher (9.8) |Staffordshire Bull Terrier (10.0) |
|English Cocker Spaniel (11.8) |Standard Poodle (12.0) |
|English Setter (11.2) |Tibetan Terrier (14.3) |
|English Springer Spaniel (13.0) |Toy Poodle (14.4) |
|English Toy Spaniel (10.1) |Viszla (12.5) |
|Flat-Coated Retriever (9.5) |Weimaraner (10.0) |
|German Shepherd (10.3) |Welsh Springer Spaniel (11.5) |
|German Shorthaired Pointer (12.3) |West Highland White Terrier (12.8) |
|Golden Retriever (12.0) |Whippet (14.3) |
|Gordon Setter (11.3) |Wire Fox Terrier (13.0) |
|Great Dane (8.4) |Yorkshire Terrier (12.8) |
Source: The pets.ca website
[See the World Almanac for information regarding the life expectancy of other anaimals. Those longevities range from about two years for mouse to about 35 years for elephant. Just thought you might like to know.]
Tidbits
Could life expectancy ever be infinite? Not according to the biological findings and arguments of Carnes, Olshansky, and Grahn (2003), for both human animals and infrahuman animals. The dramatic increases in life expectancy during the past 100 years are not likely to ever be accomplished again.
News of an income gap between the rich and poor in the United States would surprise very few, but a recent study (Murray, Kulkarni, et al., 2007) has documented another troubling divide in the country, this one in how long people can expect to stay alive. The study shows a 40-year difference between the longest-lived people in the nation (Asian American women in parts of New York, New Jersey, and Florida who live on average into their late 90s) and the shortest-lived (Native American men in six South Dakota counties who on average live only until their mid-50s).
CHAPTER 10: AGE ON OTHER WORLDS
All of the previous discussion has tacitly assumed that age on this planet (earth) was of primary interest. But how would one’s age change if one were living in some other “world”? The following chart, excerpted from Ron Hipschman’s website, will give you some indication (I have used my birthdate and my age as of August, 2007 as an example):
|[pic] |
|Want to melt those years away? Travel to an outer planet! |
|[pic] |
|This Page requires a JavaScript capable browser. |
|[pic] |
|[pic] |
|Fill in your birthdate below in the space indicated. (Note you must enter the year as a 4-digit number!) |
|Click on the "Calculate" button. |
|Notice that your age on other worlds will automatically fill in. Notice that Your age is different on the different |
|worlds. Notice that your age in "days" varies wildly. |
|Notice when your next birthday on each world will be. The date given is an "earth date". |
|You can click on the images of the planets to get more information about them from Bill Arnett's incredible Nine |
|Planets web site. |
|Top of Form |
|[pic] |
|MM |
|DD |
|YYYY |
| |
|[pic] |
|[pic] |
|[pic] |
| |
| |
| |
| |
|[pic] |
|MERCURY |
|[pic] |
|Your age is |
|[pic] Mercurian days |
|[pic] Mercurian years |
|Next Birthday [pic] |
|VENUS |
|[pic] |
|Your age is |
|[pic] Venusian days |
|[pic] Venusian years |
|Next Birthday [pic] |
|EARTH |
|[pic] |
|Your age is |
|[pic] Earth days |
|[pic] Earth years |
|Next Birthday [pic] |
| |
|[pic] |
|MARS |
|[pic] |
|Your age is |
|[pic] Martian days |
|[pic] Martian years |
|Next Birthday [pic] |
|JUPITER |
|[pic] |
|Your age is |
|[pic] Jovian days |
|[pic] Jovian years |
|Next Birthday [pic] |
|SATURN |
|[pic] |
|Your age is |
|[pic] Saturnian days |
|[pic] Saturnian years |
|Next Birthday [pic] |
| |
|[pic] |
|URANUS |
|[pic] |
|Your age is |
|[pic] Uranian |
|[pic] Uranian years |
|Next Birthday [pic] |
|NEPTUNE |
|[pic] |
|Your age is |
|[pic] Neptunian days |
|[pic] Neptunian years |
|Next Birthday [pic] |
|PLUTO |
|[pic] |
|Your age is |
|[pic] Plutonian days |
|[pic] Plutonian years |
|Next Birthday [pic] |
| |
|[pic] |
|Bottom of Form |
[pic][pic]
Neat, huh? (But note that Pluto has recently been eliminated from planet status.)
CHAPTER 11: THE MEASUREMENT OF HEIGHT
How can we measure height? Let me count the ways:
1. Stadiometer
2. Yardstick
3. Tape measure
4. Self-report
5. Eyeball
6. Back-to-back
The use of a stadiometer (sometimes called an anthropometer; anthropometry is the study of body measurement), either a vertical one (for measuring the heights of older children and adults) or a horizontal one (for measuring the heights of persons who are unable to stand or for infants--in which case it is called an infantometer) is alleged to be the most valid and reliable way to measure height (the "gold standard"). Most stadiometers are connected to weight scales and are usually found in doctors' and nurses' offices (I'm sure you've seen them and have been "heighted" and "weighted" on them). They range in price from about $68 to about $949 (see the QuickMedical website), and you usually get what you pay for; i.e., the more expensive ones are the finest. [Note: There is at least one other meaning of the word "stadiometer". The Word List Definitions of Scientific Instruments website defines a stadiometer as an "instrument for measuring the length of a curved line".]
A second approach is to use a regular household yardstick. The persons whose heights are to be taken are usually asked to stand with their backs to a wall, a mark is made on the wall at the tops of their heads, they are asked to step away from the wall, and the distance from the mark to the floor is measured with a yardstick.
The procedure for measuring height with a tape measure is the same as for a yardstick, except that the distance from the mark to the floor is measured with a tape measure.
A fourth, and most frequently used, method is simply to ask the persons how tall they are. (It is tacitly assumed that they have recently had their heights measured with a stadiometer or a yardstick or a tape measure and their recall of such a measurement is reasonably accurate.)
The eyeball method is just what it sounds like. The "measurer" looks at the "measuree" and the former records the height that the latter appears to be, usually based upon the measurer's own known height.
The back-to-back method is a variation of the eyeball method. The measurer and the measuree stand back-to-back and the measurer records a height for the measuree, again with respect to the measurer's height.
It may be a bit gratuitous to refer to these last three methods as ways for measuring height, since no measuring instruments are involved. Self-reported height will be thoroughly explored in Chapter 16 as one of several ways to estimate height. The eyeball and back-to-back methods are discussed by Keyes (1980) in his book, but to my knowledge they have never been subject to serious scientific investigation.
Use of a stadiometer to measure height
The principal user of a stadiometer (the 235 Heightronic Digital Stadiometer) is the National Health and Nutrition Examination Survey (NHANES) that began in 1971 and is still being carried out (Harris, Burt, et al., 1993; Blackburn, 2003). Every ten years or so the heights, weights, and other body dimensions of a national sample of adults and children are measured, in order to provide some indication of the general health of the nation. NHANES IV (1997-2004), which was almost scrapped (see van Houten, 1998), is based on a representative sample of approximately 40,000 of the non-institutionalized population of the United States (about 5,000 people per year drawn from 15 randomly selected locations). Through the use of a mobile exam center, subjects throughout the country are given a standardized physical exam that includes the measurement of height and weight as well as blood pressure and several other variables.
NHANES IV, like all of the other preceding surveys, has a strict protocol for body measurement. (There is an equally strict protocol for measuring the heights and weights of American Indian and Native Alaskan children--see the manual prepared for the American Indian Alaska Native Pediatric Height and Weight Study, 2001-2002; it is available on the internet.) As far as height is concerned, the NHANES anthropometry procedures manual ("downloadable" at the NHANES website) includes the following specifications [and I quote, adding a few comments in brackets]:
"Standing height is an assessment of maximum vertical size. Take this measure on all SPs [the NHANES abbreviation for Subject Persons] 2 years and older, who are able to stand unassisted. [All persons to be measured wear only light clothing and foam slippers--see the procedures for measuring weight in the following chapter.] Standing height is measured with a fixed stadiometer with a vertical backboard and a movable headboard. Have the SP move or remove hair ornaments, jewelry, buns, braids, and corn rolls from the top of the head in order to measure stature properly. ["Stature" is the more general term used instead of "height" in anthropometry.]
Have the SP stand on the floor (see Exhibit 3-1) [provided in the manual] with the heels of both feet together and the toes pointed slightly outward at approximately a 60° angle. Make sure the body weight is evenly distributed and both feet are flat on the floor. Check the position of the heels, the buttocks, shoulder blades, and the back of the head for contact with the vertical backboard. Depending on the overall conformation of the individual, all points may not touch. In such case, make sure the SP's trunk is vertical above the waist, and the arms and shoulders are relaxed.
Align the head in the Frankfort horizontal plane. The head is in the Frankfort plane when the horizontal line from the ear canal to the lower border of the orbit of the eye is parallel to the floor and perpendicular to the vertical backboard. Many people assume this position naturally, but for some it may be necessary to make a minor adjustment. If required, gently tilt the head up or down until proper alignment is achieved with eyes looking straight ahead. Once correctly positioned, lower the headboard and instruct the SP to take a deep breath and stand as tall as possible. A deep breath will allow the spine to straighten, yielding a more consistent and reproducible stature measurement. Position the headboard firmly on top of the head with sufficient pressure to compress the hair. When the SP is properly positioned, tell the recorder to "capture" the height. Hold the headpiece in position until the computer verifies the reading. [Yes, the process is computerized.] Then have the SP relax and step away from the stadiometer. In the event of a power outage or if the stadiometer is not functioning properly, push the headpiece to the top of the measurement column and obtain the subject's height using the tape measure mounted on the right side of the measurement column. Call the height to the recorder, who will enter it in the height box of the automated system.
Some SPs may have conditions that interfere with the specific procedures for measuring stature. One of the more common conditions is kyphosis. Kyphosis is a forward curvature of the spine that appears as a hump or crooked back condition. Kyphosis most frequently occurs in the elderly, and in women the condition is commonly referred to as dowager's hump [that sounds politically incorrect]. In these cases it is important to get the best measure possible according to the protocol. Then select the "NS" (not straight) comment. "
Source: NHANES Anthropometry Procedures Manual, Chapter 3, pages 21-22
Compulsive? Of course. Compulsivity [is there such a word?] is the trademark characteristic of good research and practice.
When the stature of an older child or an adult is measured, the measurement is called "height", but when the stature of an infant is measured, the measurement is called "length". The reason, of course, is that an infant is unable to stand upright for the first few months of life and therefore the measurement is taken while the baby is lying supine. Here is what the NHANES manual has to say about measuring infants:
"Recumbent length is measured on children less than 4 years of age (birth to 47 months). [Elsewhere in the manual it is indicated that children between 24 and 47 months of age are measured for BOTH standing height and recumbent length.] An Infantometer [the 447 Infantronic Digital Stadiometer] is used to take the measure. The measuring board has a fixed headpiece, a horizontal back piece, and a moveable foot piece. Placing infants and small children in a recumbent position frequently generates a sense of insecurity and consequently involves a crying response. When measuring recumbent length the parent or other caretaker of the child should be positioned between the examiner and recorder. The parent should encourage and comfort the child by making eye contact, talking to, and if necessary, holding the head of a restless child. The recorder supports the child's head. Similar to the procedure with standing height, the child's head is positioned in the Frankfort plane. Gentle traction is applied to bring the top of the head in contact with the fixed headpiece. The child's head must be firmly held in this position by gently cupping the palms of the hands over the ears and holding the head in proper alignment. Simultaneously, the examiner aligns the child's legs by placing one hand gently but firmly over the knees. The toes point directly upward with the soles of the feet perpendicular to the horizontal backpiece of the measuring device. Gentle pressure is applied at the knees to keep the legs straight. The examiner then slides the moveable foot piece to rest firmly at the child's heels. When the child is properly positioned, the recorder will click on the capture button on the screen. In the event of a power outage or if the infantometer is not functioning properly, the examiner will position the child as described above and read the length using the tape measure mounted on the board of the infantometer. The examiner will then call this measurement to the recorder, who will enter it in the recumbent length box."
Source: NHANES Anthropometry Procedures Manual, Chapter 3, page 39
Equally compulsive, and equally commendable.
Here are some excerpts from another source regarding the measurement of children's heights:
"Valid measurements are not possible without cooperation from the subject... Before beginning a session, the anthropometrist must establish a rapport with the subject. The anthropometrist should help the child and parent understand what is going to be done. A brief description of all the measurements and the equipment may help put both the child and parent at ease... The anthropometrist should not be formal, nor should he risk accurate measurements by being too relaxed... When taking the measurement, the measurer should be firm, not reluctant. People, especially children, may react negatively to an apprehensive, insecure approach... Sources of error in anthropometric procedures can be either within-observer or between-observer in origin. Interobserver (between-observer) reliability is the ability to obtain duplicate measurements on the same subject by multiple observers. Interobserver errors mainly consist of differences in which each measurer performs the technique... Intraobserver (within-observer) reliability is the ability of an observer to repeat measurements on a subject and obtain consistent values. Intraobserver errors include imperfections in the measuring instruments, the recording techniques, and the measurer's technique. Careful thought by the measurer and properly maintaining equipment can help reduce intraobserver unreliability. Because of their use in diagnosis and their importance in other medical decisions, all measurements should be reliable and valid. Reliability ensures that the measurements can be relied or depended upon; that is, they are reproducible using the same technique. Validity means that the measurements produce the desired results... All measurements require the use of a standard technique which should be reproducible. If technique is compromised for any reason during a session, the measurement should not be used... All measurements should be taken at least twice. The average of the two should be used for clinical or research purposes. Measurement techniques are the same in adults and children, but extra attention to error should be made for children. Error is likely to be higher in children because they will not cooperate and hold a position for any extended period of time."
Source: University of Virginia Children's Medical Center website
[See also the nice pictures in Jarvis's (1996) text, pp. 182-183.]
Lampl, Birch, et al. (2001) expressed serious concerns regarding the measurement of recumbent length of infants. In their study they found that between 60% and 70% of total measurement error could be attributed to factors associated with the difficulties involved in measuring infants in that position.
Most if not all bedridden patients have to have their stature measured in the supine position (see the website of the Natural History Museum of Florence, Italy for a picture of an adult horizontal stadiometer), but fortunately there are very few occasions when such a measurement is required, the determination of body surface area (BSA) being the most important reason, since it is often a key determinant of drug dosage (see Chapter 18).
Measurement of the heights of the non-bedridden elderly can also be a problem. See Haboubi, Hudson, and Pathy (1990); Harris, Burt, et al. (1993); Sullivan, Patch, et al. (1998); and the reference to kyphosis in the NHANES height protocol (above).
Use of a yardstick to measure height
The following directions for measuring children's heights with a special 6-foot "yardstick" are taken from the 54-month manual used in the Early Child Care study carried out by the National Institute of Child Health and Development (NICHD) [again, I have added a few comments]. I have chosen this excerpt in order to show that it is sometimes necessary to be as compulsive in the use of a yardstick as it is in the use of a stadiometer.
"Height is the standard method of measurement for children this age. Height will be measured at 54 months in the same way it was measured at 36 months using a "yardstick" and a t-square. Each site will use a metal [commendable] "yardstick" and a standard builder's t-square. Because children [some children?] will have outgrown the 48-inch "yardstick" that was used at 36 months, sites will use a 6-foot "yardstick" at 54 months [there must have been some pretty tall 4 1/2 year-old children in that study!]. All "yardsticks" will be identical [equally commendable] and will be purchased from the same store [unspecified].
The yardstick [no longer within quotation marks] is to be taped to a wall, preferably next to a door jam [sic]. The bottom of the yardstick (starting with 0 inches) should be flat against the floor of the room and flush against the door jam [sic again], so that the yardstick and the floor are perpendicular to each other. The yardstick should be checked before every visit to insure that it is securely attached to the floor and is positioned at a 90 degree angle to the floor. The t-square can be used to check that the yardstick is positioned vertically at a 90 degree angle to the floor. The t-square should be stored nearby so that it is accessible for the measurement procedure [overly compulsive?].
... To measure the child's height, follow these steps:
1) Tell the child that you are going to see how tall he/she is.
2) Ask the child to have the mother help the child to remove his/her shoes.
3) Ask the child to walk over to the yardstick. Tell him/her that you want him/her to turn around and back up to the wall so that his/her back is against the yardstick. Make sure that his/her heels are both touching the yardstick/wall and that the child's head is against the yardstick. The child's feet (heels and toes) should be as close together as possible. Ask the child to stand straight and tall.
4) When the child is in the correct position, place the t-square so that one arm (the shorter, plastic-coated arm [of the t-square, not the child!]) is flat against the yardstick and the other arm is perpendicular to the yardstick and positioned several inches above the child's head. The VC [their abbreviation for "visit coordinator" and not "Viet Cong", who assists with the measurement] should hold the shorter, plastic-coated arm that is flat against the yardstick when taking the measurement. Slide the t-square down the yardstick so that the bottom side of it touches the top of the child's head. (Do not simply fit the t-square into position resting on the child's head.) Be sure that the t-square is flat against the yardstick and resting lightly on the top of the child's head. Then ask the child to step away from the wall. As the child steps away from the wall hold the t-square securely against the yardstick.
If the child has a hair style which will add to the height, such as a ponytail, the mother should be asked to undo the hair in order to get an accurate measurement.
5) To read the height, look at the position where the bottom of the t-square meets the yardstick. Record the height to the last complete 1/8". (In other words, always round up [down?] to the last complete 1/8".)
6) Obtain a second measure, verifying the proper position of the child as described above prior to each measurement.
7) If the second measurement differs from the first by more than 0.25 of an inch [why didn't they say 1/4 inch?], record these heights and obtain two more height measurements according to the above procedure. [Now that's compulsive; and what if some of those differ from others by more than 0.25 in?]
8) Wipe off the yardstick and the t-square with soap and water after measurement is completed. [Good thing they're not made of wood.] "
Source: NICHD 54-month manual, pp. 7-8 and 10-11
Use of a tape measure to measure height
The following directions for measuring an infant's height with a tape measure are taken verbatim from an easily-accessible website:
"Pediatricians use several devices for measuring an infant's length (what is later referred to as height). However, it is possible to use a simple tape measure to check your baby's length at home. To obtain a correct measurement, it will be necessary to lay your baby on his or her back. Position the baby's head against a wall. Holding the baby's knees together and pressing them gently, place a tape measure from the wall down to the infant's heels. It may be necessary to have one person hold the infant while another measures. Record the baby's length in inches or centimeters. "
Source: The Children's Growth Calculator page of the Health AtoZ website
And in the first of their two articles on height measurement, Dr. Jean Brown and her colleagues (Brown, Whittemore, & Knapp, 2000) described the procedure they used for measuring adult heights with a tape measure. [I am privileged to have been part of that research team]:
"Height was measured twice to determine test-retest reliability. Subjects were asked to remove their shoes, stand facing away from and against the wall [buttocks, back, and head against the wall] and hold their head erect in the Frankfort horizontal plane as shown in Figure 1. A carpenter's square [Empire model 1190, Milwaukee, WI] was placed against the wall and head, the subject was asked to step away from the wall, and height was measured from the floor to the bottom of the square with a metal rule [Stanley model 33-158, New Britain, CT]. Measurements were read to the nearest 0.1 cm." (p. 87)
Both of those excerpts were chosen to illustrate that the measurement of height with a tape measure also requires standardization and care.
Validity and reliability of methods for measuring height
Stadiometers
At the beginning of this chapter I said that the stadiometer is "alleged" (an important word) to be the most valid and reliable way to measure height. But what is the evidence for that claim? And what is the difference between valid and reliable?
Let me answer the second question first. A measuring instrument is said to be valid if it "really" (a difficult word) measures what it is intended to measure. A measuring instrument is said to be reliable if it measures consistently whatever it is that it measures, i.e., whether or not it is valid. [These terms were used in the second excerpt regarding the measurement of infant length with a stadiometer--see above. For a good discussion of the reliability of physical measures, see Engstrom (1988); for an interesting summary of alternative terms for validity and reliability, see Feinstein (1985, 1987); and for more than you ever wanted to know about reliability and validity, see my 1985 article and the Measurement chapter in my nursing research text (Knapp, 1998). We would all agree (wouldn't we?) that to try to measure someone's height with a barometer would not be valid, because a barometer measures air pressure, not height, and does so reliably (consistently). [But see the hilarious piece on the Science Jokes 2 website concerning various suggestions for using a barometer to measure the height of a building!]
Regarding the first question, a stadiometer looks like it measures height (so-called "face validity") and the experts (the anthropometrists) tell us that it does. Other than that, we have little or no evidence for its validity for measuring height.
In order to determine the reliability of any instrument that is alleged to measure height we need actual data, i.e., expert judgment isn't good enough. [We should be careful with claims based upon expert judgment, anyhow, and if possible we should try to get some empirical data regarding their alleged expertise--see Weiss and Shanteau (2003a, 2003b).] How does the stadiometer perform regarding reliability? The manufacturers of some stadiometers often refer in their advertisements to statements such as "The Height-Rite™ [vertical stadiometer] will accurately measure patients to within the nearest millimeter or sixteenth of an inch" and "the Infantronic [horizontal stadiometer] gives you a digital readout accurate to 0.1 millimeter”, but they do not provide the results of actual studies of human beings where the reliabilities of their instruments were calculated. There are reports in the literature of a few such studies (see the following paragraphs), but most investigators who use stadiometers tacitly assume that they are the "gold standards" for measuring height and need not be subject to empirical investigation. I disagree (with the latter claim).
For a sample of 229 subjects (95 male, 134 female) in NHANES II, Marks, Habicht, and Mueller (1989) found the measure/re-measure correlation (reliability coefficient) of a height stadiometer to be very high (a correlation of approximately .97).
Voss, Bailey, et al. (1990) measured ten children three times each with five different stadiometers. The children's "true" heights ranged from 106.0 cm to 152.0 cm. The average difference from true height was about .2 to .3 cm.
In a study carried out by Rodacki, Fowler, et al. (2001), ten subjects (five males and five females) had their standing heights measured with a stadiometer 150 times each [wow!], in 3 series of 10 sets of 5 measurements, with "breaks" between the series for the subjects to get off and then back on the stadiometer. (See their article for more details and for some great pictures.) The average discrepancy between one measure and another ("un"reliability) was of an order of magnitude of approximately one-half millimeter. (Again see their article for more details--the analysis was rather complicated--and for a comparable discussion of their findings regarding the measurement of the sitting heights of ten other subjects.)
Dr. Janet Engstrom and her colleagues have carried out several investigations of the reliability of infantometers (and of tape measures--see below) for measuring the supine length of newborns. They concentrate on absolute measures of reliability, such as average discrepancies between corresponding measurements, rather than correlations between two sets of measurements, because, as she (Engstrom, 1988) and others (e.g., Rogosa, 2002; Baker & Kramer, 2003) have argued, you can get a perfect correlation between two sets of measurements, e.g., 1, 2, 3, 4, 5 and 10, 20, 30, 40, 50, yet have very poor agreement between the actual magnitudes of the measurements. Here are some of their findings:
Johnson, Engstrom, et al. (1998): Using the Neo-infantometer for a sample of 32 babies, the within-examiner mean absolute discrepancy (intra-examiner reliability) was .50 cm for one examiner and .71 cm for a second examiner. The between-examiner mean absolute discrepancies (inter-examiner reliability) were .81 cm for the first comparison between the two examiners (Examiner A's first set of measurements vs. Examiner B's first set of measurements) and .61 cm for the second comparison (of their second sets of measurements).
Johnson, Engstrom, et al. (1999): Using the Auto-lengthTM measuring device for a sample of 48 healthy term infants, the intra-examiner reliabilities for two examiners were .60 cm and .84 cm, respectively; and their inter-examiner reliabilities were 1.02 cm and .82 cm. [They reported evidence regarding the technical error of measurement (Engstrom, 1988; Knapp, 1992)--sometimes called the standard error of measurement--for the infant stadiometers used in their studies, in addition to the evidence just summarized. The Engstrom articles also include some excellent summaries of the proper use of such infantometers.]
For references to some older studies of the reliability of infant stadiometers, see Table 1 in the Johnson, Engstrom, and Delhar (1997) article. And if you're interested in the history of the measurement of infant length, see the excellent article by Johnson and Engstrom (2002).
Yardsticks
Yardsticks seem to play a strange role in the measurement of height. Serious health professionals and researchers never use them--writing them off as hopelessly inadequate scientifically--whereas ordinary people use them all of the time to measure height, particularly of their growing children. But how valid and reliable are they?
Just as is the case for stadiometers, yardsticks look like they should provide good measurements of height (face validity again) and they should yield similar results for a person who is measured twice in a very brief time period (say a minute or two) with the same yardstick by the same measurer, and should also yield similar results for a person who is measured by two different measurers within an equally brief time period. But what is the evidence? I could find no sources that reported the results of empirical studies in which people were measured at least twice with the same yardstick, so that the reliability of the yardstick could be determined. [In my reliability book (Knapp, 2007) I include a set of artificial data for which the reliability of a yardstick is abysmal!]
Tape measures
As I indicated above, some of Engstrom's studies were also concerned with the reliability of tape measures for measuring infant length. For a sample of 48 infants measured twice by each of two registered nurses, Rosenberg, Verzo, et al. (1992) found a mean absolute difference between first and second measurements of .64 cm for Nurse 1 (intra-measurer reliability), a mean absolute difference of .50 cm for Nurse 2 (also intra-measurer reliability), a mean absolute difference of .89 cm between their first measurements (inter-measurer reliability), and a mean absolute difference of .84 cm between their second measurements (also inter-measurer reliability). Johnson, Engstrom, & Delhar (1997) reported mean intra-examiner absolute differences of .92 cm and 1.18 cm for two examiners who measured a sample of 50 newborns twice each; the corresponding inter-examiner statistics were .74 cm and .84 cm. Johnson, Engstrom, et al. (1998) reported average intra-examiner discrepancies of .80 cm and .53 cm, and average inter-examiner discrepancies of .74 cm and .84 cm for a sample of 32 babies. And Johnson, Engstrom, et al. (1999) reported intra-examiner reliabilities of .92 cm and .74 cm, and inter-examiner reliabilities of 1.13 cm and 1.39 cm (n = 48).
The first study carried out by Brown and her colleagues (Brown, Whittemore, & Knapp, 2000--see above) provided some evidence for the reliability of tape measures for measuring height. They found a measure/re-measure reliability coefficient of .998 and a mean absolute difference of .20 cm for the Stanley model 33-158 tape measure. In their second study (Brown, Feng, & Knapp, 2002) the measure/re-measure reliability coefficient was .997 and the mean absolute difference was .43 cm.
One of the best studies of the validity (they call it reliability) of devices for measuring infant length is the research reported by Byrne and Lenz (2002). They compared three instruments: an ordinary cloth tape measure, a portable device (the Measure Mat), and a traditional stationary infantometer (the Fairgate Rule stadiometer). For the tape measure they found a mean absolute difference (between the tape measure and the infant stadiometer) of 1.75 in for one sample of 30 infants and a mean absolute difference of 1.05 in for a second sample of 15 infants.
In an interesting study of 28 parents' ability to make accurate measurements of their infants' recumbent length (RL) and other anthropometric variables, Bradley, Brown, and Himes (2001) found that for RL the correlation with measurements made by a trained observer was a disappointing .81.
In addition to the sources just cited I found one unsupported claim regarding the reliability of a particular tape measure (the Talking Tape Measure [yes, Virginia, there is such a thing!]) on the Dynamic Living website: "You don't have to struggle to see the numbers, for this 16 foot metal tape measure announces the measured length with an accuracy of 1/16th of an inch."
Method comparison studies
Some researchers, e.g., Altman and Bland (1983); Bland and Altman (1986, 1999, 2002); Szaflarski and Slaughter (1996), regard certain studies as "method comparison" studies, where two or more measuring procedures are compared with one another but the instruments are not "parallel" forms (which is necessary for reliability) and one of the instruments is not taken to be the "gold standard" (which is necessary for validity).
Units of measurement
Does it matter whether height is measured in feet and inches, in inches only, in meters, or in centimeters? Not really, since each of these can be converted to any of the others by using simple linear transformations or by referring to readily-available tables (1 inch = 2.54 centimeters; 1 centimeter = .394 inches; 1 meter = 100 centimeters; 1 centimeter = .01 meters), but some people are rather fussy about this. Most Europeans and most scientists favor the metric system, whereas most ordinary Americans favor the British ("Imperial") system. I am both a scientist and an ordinary American. I favor the British system of feet and inches; I just can't get used to thinking of height in terms of meters or centimeters. But I recommend that you read the pro and con arguments on this topic at the O Pine Forum website and draw your own conclusions. And see Berman (2000), who described an unfortunate incident in September, 1999 when some people at NASA mixed up the two systems!
Interestingly, the distributions of the heights of older children and adults who participated in NHANES III (1988-1994) were reported in inches whereas the distribution of recumbent lengths of infants who participated in that survey were reported in centimeters [rather than fractions of inches, I guess]. For more regarding those distributions, see Chapter 13.
If you think about it, the heights of human beings could be measured in terms of "hands", just like the heights of horses are. (A "hand" is equal to four inches.) For a fascinating discussion of the origins of the "hand", the "yard", etc., see The Hand Measurement webpage on the Ontario, Canada Ministry of Agriculture and Food's website.
A platinum standard?
There has been recent research and development work on three-dimensional surface anthropometry that would provide height, weight, and other body measurements "in one fell swoop", so to speak. (See, for example, Jones & Rioux, 1997 and/or any of the other articles in that special issue of Optics and Laser Engineering.) That would make such a device "the new gold standard" for the measurement of height and weight (and body mass index and body surface area, as well as other dimensions that are presently determined one variable at a time.)
CHAPTER 12: THE MEASUREMENT OF WEIGHT
There are only two defensible ways for measuring weight, and they are:
1. Top-quality weight scale
2. Ordinary bathroom scale
[Self-reported weight will be treated in Chapter 16, along with self-reported height. The analogue to the eyeball method for "measuring" height, i.e., the eyeball method for "measuring" weight, is only used at carnivals--as far as I can tell. If you're interested in that, see the delightful article in the July 28, 2001 issue of the Goshen, Indiana News (accessible at its website) about Ray DeFrates, who had been guessing people's weights at carnivals for 50 years! And there is no weight analogue to the back-to-back method for height. The closest thing is the measurement of the weight of a small person by holding him(her) in your arms as you weigh both of you on a scale, then weighing yourself only, then subtracting the latter weight from the former weight.]
The use of top-quality weight scales
Top-quality weight scales are often attached directly to stadiometers, and the best ones (a balance beam scale, which can be zeroed after each measurement, is usually taken to be the "gold standard") cost almost $1000. Not surprisingly, NHANES is the principal user of top-quality scales in their periodic anthropometric surveys. Their procedures manual has this to say regarding how they measure weight (with my comments in brackets):
" The SP's weight will be taken on a Toledo digital scale [not attached to a stadiometer]. Weight will be measured in pounds and converted to kilograms in the automated system. Infants should wear only diapers and children and adults should wear only underwear, disposable paper gowns, and foam slippers. (Women should wear underpants only.) Infants and toddlers who can't stand unassisted will be weighed with an adult. Have the parent or technician stand alone on the platform, tare the scale [? I thought the term "tare" was only used in conjunction with tractor-trailers hauling freight?], and have the person on the scale hold the infant or toddler to obtain only the child's weight [by subtraction of the holder's known weight]. Holding the child will provide greater security and reduce movement that might otherwise affect the accuracy of the measurement. Instruct older children and adults to stand still in the center of the scale platform facing the recorder, hands at side, and looking straight ahead. When the SP is properly positioned and the digital readout is stable, the recorder will click on the capture button on the [computer] screen. If the examinee weighs more than 440 pounds, use two Seca digital scales (located in the fourth drawer of the cabinet), have the SP stand with one foot on each scale, and add the weight on each scale to obtain an approximation of their weight. [Now that's clever, but does it really work??] Enter this into the weight box of the screen. Do not weigh examinees in torso casts, but ask them to estimate their weight [huh?] and then document this estimation in the comment section of the automated system. In the event of a power outage [I wonder how often that has ever happened] or if the scale is not functioning properly, use a Seca digital scale. Turn the scale on by pressing the "On" button [how compulsive can you get!], and have the SP stand on the scale as described above. Call the weight to the recorder, who will enter it into the weight box of the automated system."
Source: NHANES Anthropometry Procedures Manual, Chapter 3, pages 20-21
Although NHANES uses a top quality Toledo scale and "the subtraction method" for weighing an infant (weight of adult plus infant minus weight of adult equals weight of infant), there are special pediatric scales available (e.g., the Tanita BD-585 Portable Digital Infant Scale) for weighing an infant directly (see the picture in Jarvis, 1996, p. 181).
The use of ordinary bathroom scales
These scales are considerably less expensive (around $50 or so for a reasonably good one). But care must also be taken when using them. I reproduce the following information from a recent Tanita ad for its 1623 Bathroom Scale:
|[pic] |[pic] |[pic] |Note: "Lo" will appear as a warning when |
|Step on the scale. There |When the display changes |Step off the scale and your|batteries are running low. When they are |
|are no buttons to push or |from 888 to 000, a "beep" |weight appears. Results are|completely used up, the display may remain |
|switches to activate. |signals that weighing is |displayed for about 10 |blank. For best results, replace batteries |
| |complete. |seconds. |promptly. When not used for prolonged periods |
| | | |of time, remove the batteries. For accurate |
| | | |results, place the scale on a hard flat |
| | | |surface; it will not function properly on |
| | | |thick carpeting or rugs. |
|Specifications: | |
| | |
|Maximum Capacity: | |
|300lbs/1lb graduations | |
| | |
|Power Supply: | |
|DC 6V, AAA (UM-4) batteries x4 (not included) | |
| | |
|Product Colors: | |
|White | |
| | |
Validity and reliability of methods for measuring weight
Empirical investigations of the validity and/or reliability of weight scales (both top-quality scales and ordinary bathroom scales) are even more scarce than their height counterparts. For the "gold standard" scales there appears to be the same acquiescence to the experts and to the manufacturers that such scales are both valid and reliable. And researchers consider ordinary bathroom scales as inferior for measuring weight as yardsticks are for measuring height.
The best empirical studies of the reliability of weight scales have been carried out by Engstrom and her colleagues, often in conjunction with their studies of the reliability of instruments for measuring infant length. Johnson, Engstrom, & Delhar (1997) used an electronic scale (Smart Scale Model 20, Olympic Medical; Seattle, WA, U.S.A) to measure the weights of a sample of 50 infants. To quote from their article: "This scale integrates the activity level of an infant by automatically taking 10 weights in rapid succession. A mean of the 10 weights is calculated and displayed as a digital readout. “ (p. 500) They found very small mean absolute differences (intra-examiner 1.88 and 3.28 g; inter-examiner 1.94 and 1.66 g).
In a set of three related articles, Kavanaugh, Meier, & Engstrom (1989), Kavanaugh, Engstrom, et al. (1990), and Meier, Lysakowski, et al. (1990) reported the results of a study of the weighing of a sample of 50 infants with two types of scales (a traditional mechanical scale and a an electronic SMARTTM scale). They investigated both intra-measurer and inter-measurer reliability. For the former they found a mean absolute difference of 5.50 g for the mechanical scale and a mean absolute difference of 1.36 g for the electronic scale. For the latter they found a mean absolute difference of 18.00 g for the mechanical scale and a mean absolute difference of .88 g for the electronic scale. (As in several of their studies of infant length they also reported the technical error of measurement and other indicators of the reliability of the two types of scales.)
In two later studies of the measurement of weight for atypical infants, Meier, Engstrom, et al. (1994) and Engstrom, Kavanaugh, et al. (1995) investigated the measurement properties of the BabyWeighTM electronic scale and two SMART scales (Model 20 and Model 35). The former study was concerned with the validity of the BabyWeigh scale for in-home weighing of 30 preterm and/or high risk infants, using the SMART Model 20 scale as the "gold standard". The mean absolute difference between corresponding measurements for the two scales was 1.30 g. The latter study was concerned with the reliability of the SMART Model 35 scale for the in-bed weighing of 32 critically ill infants. They provided several summary statistics for both intra-measurer and inter-measurer reliability (there were four examiners who took the measurements). The mean absolute intra-measurer difference was 12.58 g for weights obtained in the incubator and was 19.19 g for weights obtained under the radiant warmer; the corresponding mean absolute intermeasurer differences were 14.29 g for incubator and 24.42 g for radiant warmer.
For references to some older studies of the reliability of weight scales, see Table 1 in the Johnson, Engstrom, and Delhar (1997) article. And for an excellent discussion of the history of the measurement of infant weight, see Johnson and Engstrom (2002).
Weight vs. mass
Physical scientists make a distinction between weight and mass. The former takes into account the force of gravity, while the latter does not. Two people of identical mass will have slightly different weights if, for example, one is weighed in Denver, Colorado and the other in Death Valley, California. The Coloradan would weigh less since the force of gravity is less at higher elevations than at lower elevations. It is even less at the poles. [What a great way to lose weight! Move from Death Valley to Antarctica!!] The difference in my weight in Hawaii (I actually live there), in Denver, in Death Valley, or in Antarctica would actually be rather tiny, since the force of gravity is approximately constant anywhere on earth. But if I were to move to the sun or to the moon or to one of the other planets, my weight of 150 pounds would change rather dramatically in most of those locations, as follows (all in pounds):
Sun: 4060.8
Moon: 24.9
Mercury: 56.7
Venus: 136
Mars: 56.5
Jupiter: 354.6
Saturn: 159.6
Uranus: 133.3
Neptune: 168.7
Pluto: 10 [N.B. As indicated previously, Pluto is no longer “officially” recognized as a planet.]
Source: Ron Hipschman's exploratorium.edu/ronh/weight website]
If you want to determine how much you would weigh in various places, take your earth weight (= your mass) and multiply it by the approximate forces of gravity relative to earth's 32 feet (= 9.8 meters) per second per second.
To calulate your weight: mass x gravity = weight
|Location |Mass |Gravity |Weight |
|Earth |blank |1 |Blank |
|Outer space |blank |0 |Blank |
|Earth's moon |blank |0.17 |Blank |
|Venus |blank |0.90 |Blank |
|Mars |blank |0.38 |Blank |
|Mercury |blank |0.38 |Blank |
|Jupiter |blank |2.36 |Blank |
|Saturn |blank |0.92 |Blank |
|Uranus |blank |0.89 |Blank |
|Neptune |blank |1.13 |Blank |
|Pluto |blank |.07 |Blank |
Source: Science Court website [N.B. The figure for Saturn may be in error.]
Note that whatever your mass is on earth, when you multiply it by the gravity constant for outer space of zero you get zero (and thus the concept of "weightlessness"). So an even greater way to lose weight is to go to outer space! In the process of losing weight you will also gain height--something on the order of 6 to 8 centimeters. [See Lujan & White's (no date) book, Human physiology in space, regarding this, especially their section on Bone Function. In that section they include a neat graph showing how the heights in outer space of certain astronauts differed from their greatest early morning heights on earth. In early morning people's heights are at a maximum; by late evening they can be less by about a half-inch or so.]
Units
Just as is the case for heights, weights can be measured in either metric units (kilograms) or Imperial units (pounds), where one pound = 2.2046 kilograms; one kilogram = .4536 pounds (ignoring the difference between mass and weight). Take your pick. NHANES provides both. Many British people like to talk about weights in terms of "stone", perhaps because the "pound" is their principal unit of money. A "stone" is equal to 14 pounds. (For the world's greatest table for converting from one unit to another, see Bo Johansson's Measurement Conversion 1 webpage.)
CHAPTER 13: THE DISTRIBUTION OF HEIGHT
The claim is usually made that height is approximately normally distributed in most populations and in random samples taken therefrom, but there have been some recent objections to that claim. Some even argue that the distribution is bimodal--two "peaks" at height measurements of greatest frequency--when the group of persons being measured consists of males and females combined. [Who would ever want to put male and female heights in the same frequency distribution?] But the latter claim has been refuted by Schilling, Watkins, and Watkins (2002), who proved that such a distribution can only be bimodal if the difference between the male mean and the female mean is greater than the sum of their respective standard deviations (which it almost never is).
Data from NHANES III
The following sets of frequency distributions of height (all in inches except for infant lengths) have been taken directly from tables for the 1988-1994 NHANES III survey (total n = 31311: 14986 males, 16325 females). Similar information from the same survey is provided by Kuczmarski, Kuczmarski, & Najjar (2000) for older Americans (ages 60+), with a breakdown by both sex and ethnicity. [The NHANES IV data were not yet available when I first wrote this chapter, but some of those data are contained in the appendix to Chapter 18.] My comments will follow after each set.
Adult males: Percentiles
Ages: 5th 10th 15th 25th 50th 75th 85th 90th 95th
20-29 (n = 1631) 64.4 65.6 66.4 67.4 69.2 71.5 72.6 73.1 74.0
30-39 (n = 1481) 64.9 66.0 66.6 67.6 69.5 71.5 72.6 73.6 74.4
40-49 (n = 1226) 64.7 65.6 66.3 67.5 69.4 71.4 72.2 73.0 74.1
50-59 (n = 855) 64.7 65.7 66.4 67.4 69.3 71.0 71.9 72.5 73.5
60-69 (n = 1176) 63.9 65.1 65.9 66.8 68.6 70.5 71.5 72.0 72.9
70-79 (n = 875) 63.5 64.3 64.8 65.8 67.7 69.5 70.5 71.1 72.2
80+ (n = 699) 62.0 63.1 63.9 64.8 66.7 68.6 69.6 70.4 71.1
[The alert readers (Dave Barry's favorite expression) among you will have observed that this is not the way frequency distributions are usually displayed, but it works nicely for height data, since you can see at a glance how the medians (the 50th percentile points), for example, increase slightly from the 20-29 to the 30-39 age brackets and then gradually decrease thereafter. Keep in mind, however, that these are cross-sectional data, i.e., they are not for the same people, which suggests not that men get shorter as they grow older (although that may also be true) but that men who were born later (and survived) were taller.]
If you would like to display the frequency distribution of height for the above NHANES sub-samples or for any of the other sub-samples in the traditional format, you can do the following: (1) Set up some convenient number, e.g., 9, of intervals, with the first and the last intervals designated as "less than x" (where x is the 5% point) and "greater than y" (where y is the 95% point), respectively; (2) assume that the heights were equally distributed for each .1 in within the NHANES III intervals; and (3) determine the frequency for each interval by using the above data. For example, for males age 40-49:
Interval Frequency
74.1 5% of 1226 = 61
Total = 61+99+135+211+213+207+162+77+61 = 1226
The distribution appears to be pretty close to normal (it's actually a bit more platykurtic, i.e. flatter, than the normal), although you can "make" a distribution more or less normal by the way you choose the intervals.
[Alternatively, you could access the NHANES III raw data, as I did for a couple of analyses I refer to in Chapter 15, and construct the distribution "from scratch", so to speak. I don't recommend that you do that, however, since the raw data set is huge (almost 400 megabytes!) and rather difficult to use.]
It is of some interest to compare the frequency distributions of the heights of adult males in the NHANES III sample with the corresponding distributions for adult males in the NHANES I 1971-1974 sample (Abraham, Johnson, & Najjar, 1979). Here are some of the percentiles for one of the earlier distributions for White males 25-34 years of age (n = 672), in inches [the reason for my choice of this particular set of percentiles will be provided in Chapter 16 in conjunction with the estimation of the heights of historical populations]:
5th percentile: 65.3
10th percentile: 66.3
25th percentile: 67.7
50th percentile (median): 69.7
75th percentile: 71.7
90th percentile: 73.4
95th percentile: 74.3
Although the age intervals for NHANES I and NHANES III are not the same, the 15th and 85th percentiles are not available for NHANES I, and these data are for White males only, the differences between these values and the values for the corresponding percentiles in the NHANES III table (above) for adult males 20-29 and 30-39 are small. For example, the median of 69.7 is greater but fairly close to the 69.2 and the 69.5 for the NHANES III distributions. The reason for the discrepancy would appear to be the fact that the 25-34 Black males in NHANES I were about an inch shorter than their White counterparts (50th percentile = 68.6 vs. 69.7). That runs counter to the popular perception that Blacks are taller than Whites, doesn't it?
Adult females: Percentiles
Ages: 5th 10th 15th 25th 50th 75th 85th 90th 95th
20-29 (n = 1867) 59.7 60.8 61.3 62.2 64.0 66.0 67.0 67.6 68.6
30-39 (n = 1863) 59.9 60.9 61.6 62.5 64.4 66.2 67.1 67.8 68.9
40-49 (n = 1371) 59.8 60.9 61.6 62.4 64.0 65.8 66.8 67.2 68.1
50-59 (n = 1009) 59.6 60.6 61.2 62.0 63.8 65.4 66.3 67.1 67.8
60-69 (n = 1177) 59.1 60.0 60.7 61.4 63.1 64.9 65.6 66.3 67.5
70-79 (n = 988) 58.0 59.0 59.9 60.6 62.2 64.0 64.9 65.4 66.1
80+ (n = 792) 56.6 57.6 58.3 59.4 61.1 62.8 63.7 64.4 65.2
[I don't know about you, but these distributions strike me as shifted to the left more than I had expected they would be, i.e., those women were in general shorter than I thought. Perhaps it is the effect of osteoporosis in older women (median of 61.1" for the 80+ group, for example) and/or because I was used to seeing so many women in high heels?]
Males, 2-19: Percentiles
Single years of age: 5th 10th 15th 25th 50th 75th 85th 90th 95th
2 years (n = 589) 33.3 33.9 34.4 34.8 35.8 36.9 37.5 37.8 38.6
3 years (n = 513) 36.2 36.6 36.9 37.5 39.1 40.2 40.8 41.1 41.6
4 years (n = 551) 38.6 39.3 39.6 40.4 41.4 42.5 43.3 43.8 44.6
5 years (n = 497) 41.0 41.9 42.3 42.8 44.2 45.4 46.4 47.0 47.8
6 years (n = 283) * 43.9 44.1 45.1 46.8 48.5 49.3 50.0 *
7 years (n = 270) * 46.5 47.3 47.8 49.6 51.6 52.6 53.1 *
8 years (n = 269) * 48.7 49.3 49.8 51.7 53.3 54.0 55.0 *
9 years (n = 280) * 51.0 51.6 52.4 54.1 55.9 57.5 57.9 *
10 years (n = 297) * 52.9 53.3 54.4 56.3 57.6 58.7 59.9 *
11 years (n = 285) * 54.6 55.1 56.5 58.0 59.6 60.9 62.0 *
12 years (n = 207) * * 58.2 59.1 60.8 63.9 65.1 * *
13 years (n = 190) * * 60.1 61.1 63.7 66.3 67.3 * *
14 years (n = 191) * * 64.0 64.8 66.6 68.5 69.4 * *
15 years (n = 188) * * 64.8 66.0 67.8 70.8 71.7 * *
16 years (n = 197) * * 65.9 67.1 69.0 70.7 72.5 * *
17 years (n = 196) * * 66.3 68.0 69.5 71.9 73.5 * *
18 years (n = 176) * * 66.3 68.0 69.3 71.8 73.3 * *
19 years (n = 169) * * 67.0 67.6 69.1 70.5 71.4 * *
[In the tables from which these data and the following two sets of data were taken (NHANES III Tables 10 and 16) the note regarding the asterisk reads: "Figure does not meet standard of reliability or precision." I'm not sure what that means. It probably refers to reliability in the sampling sense, i.e., that the sample size was too small for certain ages to provide a good "fix" for some of the lowest and the highest percentiles, particularly the lowest and highest percentiles--see Guo, Roche, et al. (2000). The precision should be the same for all heights and all ages. But note how similar the 17 years and 18 years distributions are, and how the higher percentiles drop between 18 years and 19 years. Sampling flukes?]
Females 2-19: Percentiles
Single years of age: 5th 10th 15th 25th 50th 75th 85th 90th 95th
2 years (n = 589) 32.6 33.1 33.6 34.2 35.1 35.6 37.2 37.7 38.2
3 years (n = 590) 35.9 36.5 36.9 37.4 38.7 39.9 40.6 41.0 41.7
4 years (n = 535) * 38.7 39.4 40.2 41.3 42.7 43.4 43.9 *
5 years (n = 557) * 41.4 41.9 42.5 44.1 45.4 46.4 47.1 *
6 years (n = 274) * * 43.9 45.1 46.5 48.1 48.9 * *
7 years (n = 275) * * 46.7 47.4 48.6 50.4 51.5 * *
8 years (n = 247) * * 49.3 50.2 51.7 53.3 54.1 * *
9 years (n = 282) * 50.6 50.9 52.2 53.7 55.0 56.1 56.6 *
10 years (n = 262) * * 53.3 54.1 56.1 58.2 59.3 * *
11 years (n = 275) * * 56.4 56.8 59.5 61.0 61.8 * *
12 years (n = 239) * * 58.1 59.3 61.2 63.4 64.6 * *
13 years (n = 225) * * 59.8 61.1 62.9 64.8 66.0 * *
14 years (n = 226) * * 60.9 61.5 63.6 65.6 66.5 * *
15 years (n = 201) * * 62.1 62.7 64.1 65.7 66.5 * *
16 years (n = 221) * * 62.0 62.6 64.1 65.5 66.4 * *
17 years (n = 217) * * 61.3 62.6 64.3 65.8 67.3 * *
18 years (n = 193) * * 61.0 62.2 64.4 66.0 67.0 * *
19 years (n = 194) * * 61.4 62.4 64.8 66.4 66.9 * *
[The medians increase monotonically from age 2 to age 19 but some of the percentile points do not, e.g., the 15th percentile increases up to age 15 and then decreases until age 19 when it increases again. Another sampling fluke? And it's interesting that the sample size of 282 for the 9-year-old girls was sufficiently large for reliable/precise estimation of the 10th and 90th percentiles, but the sample sizes of 247 for the 8-year-old girls and 262 for the10 year-old girls were not. (Pretty sensitive stuff?) Aren't you glad that NHANES provided these fascinating data and that I passed them along to you?!]
Infant males (hts in cm): Percentiles
Ages: 5th 10th 15th 25th 50th 75th 85th 90th 95th
3-5 mos. (n = 291) * 60.4 61.2 62.0 64.2 66.5 67.3 68.0 *
6-8 mos. (n = 321) * 66.1 67.1 67.9 69.8 71.7 72.5 73.5 *
9-11 mos. (n = 277) * 70.0 70.9 71.8 73.6 75.6 76.6 78.0 *
1 year (n = 657) 74.5 75.6 76.8 78.4 82.1 85.5 87.1 88.1 90.0
2 years (n = 616) 85.0 86.2 87.5 88.8 91.6 94.5 96.1 97.1 99.2
3 years (n = 508) 93.4 94.2 95.1 96.7 100.1 103.0 104.1 105.7 106.9
[The most interesting thing (to me, anyhow) about these distributions and the following set of distributions for recumbent length is to compare the last two rows with the first two rows of the ages 2-19 distributions for standing height (see above), taking into account that these are in terms of centimeters and the other distributions are in inches. The median standing height for the 589 2-year-old boys was 35.8 in, which is equal to 90.9 cm; the median recumbent length for the 616 2-year-old boys was 91.6 cm. Is that difference of .7 cm attributable to sampling variability (different children and different sample sizes), to measurement error (stadiometer vs. infantometer), or both? (The corresponding medians for the 3-year-olds were 99.3 cm for standing and 100.1 cm. for recumbent.)]
Infant females (hts in cm): Percentiles
Ages: 5th 10th 15th 25th 50th 75th 85th 90th 95th
3-5 mos. (n = 309) * 58.5 59.6 60.9 62.8 64.5 65.5 66.1 *
6-8 mos. (n = 264) * * 65.1 66.3 67.8 69.7 70.6 * *
9-11 mos. (n = 316) * 68.6 69.0 70.0 72.0 73.6 74.6 75.5 *
1 year (n = 636) 73.6 75.0 76.0 77.5 80.6 83.8 86.0 87.0 88.4
2 years (n = 598) 83.8 85.1 85.9 87.7 90.1 93.9 95.6 96.5 97.8
3 years (n = 585) 92.0 93.7 95.2 96.4 99.4 102.5 104.1 105.1 107.0
[The infant girls are uniformly shorter than the infant boys at all age levels and at all percentile points except for the 95th. Exercise for the reader: Compare the median standing heights for the 2- and 3-year-old girls with the median recumbent lengths for the corresponding ages.]
Halls
Dr. Steven Halls has some interesting height data on his website (halls.md). The "Baby Bag" website lists average heights for boys and for girls in the 3 months to 13 years age range. And the website (the fp is for "family practice") provides the following information:
Normal Heights for Boys:
A. Age 1 year: 28-32 inches, mean: 76 cm (30 in)
B. Age 2 years: 33-37 inches, mean: 88 cm (35 in)
C. Age 3 years: 36-41 inches, mean: 95 cm (38 in)
D. Age 4 years: 38-44 inches, mean: 103 cm (41 in)
E. Age 5 years: 40-47 inches, mean: 110 cm (44 in)
F. Age 6 years: 43-50 inches, mean: 116 cm (46 in)
G. Age 7 years: 45-53 inches, mean: 121 cm (48 in)
H. Age 8 years: 47-55 inches, mean: 127 cm (51 in)
I. Age 9 years: 49-57 inches, mean: 132 cm (53 in)
J. Age 10 years: 51-59 inches, mean: 137 cm (55 in)
K. Age 11 years: 53-61 inches, mean: 143 cm (57 in)
L. Age 12 years: 54-64 inches, mean: 150 cm (60 in)
M. Age 13 years: 56-67 inches, mean: 156 cm (62 in)
N. Age 14 years: 57-70 inches, mean: 163 cm (65 in)
O. Age 15 years: 60-72 inches, mean: 169 cm (68 in)
P. Age 16 years: 62-73 inches, mean: 173 cm (69 in)
Q. Age 17 years: 63-74 inches, mean: 68 inches
R. Age 18 years: 177 cm (71 in)
[Why just one height for 18-year-old boys? Is that a mean?]
Normal Height for Girls:
A. Birth: 18.5-21.1 inches, mean: 50 cm (20 in)
B. Age 1 years: 27-31 inches, mean: 73 cm (29 in)
C. Age 2 years: 32-37 inches, mean: 85 cm (34 in)
D. Age 3 years: 35-40 inches, mean: 95 cm (38 in)
E. Age 4 years: 38-44 inches, mean: 103 cm (41 in)
F. Age 5 years: 40-47 inches, mean: 108 cm (43 in)
G. Age 6 years: 43-49 inches, mean: 115 cm (46 in)
H. Age 7 years: 45-52 inches, mean: 120 cm (48 in)
I. Age 8 years: 47-54 inches, mean: 125 cm (50 in)
J. Age 9 years: 49-56 inches, mean: 130 cm (52 in)
K. Age 10 years: 50-59 inches, mean: 138 cm (55 in)
L. Age 11 years: 52-62 inches, mean: 143 cm (57 in)
M. Age 12 years: 54-65 inches, mean: 150 cm (60 in)
N. Age 13 years: 57-66 inches, mean: 155 cm (62 in)
O. Age 14 years: 58-67 inches, mean: 158 cm (63 in)
P. Age 15 years: 59-68 inches, mean: 158 cm (63 in)
Q. Age 16 years: 59-68 inches, mean: 159 cm (64 in)
R. Age 17 years: 60-68 inches, mean: 160 cm (64 in)
[They provide a range of normal heights (lengths) at birth for girls but not for boys. I wonder why. And why no data at all for 18-year-old girls?]
Joiner's data
In his fascinating article, Brian Joiner (1975) provided a photograph of a "living histogram" of 123 female students at Pennsylvania State University standing on a football field. The frequency distribution of their heights, in inches (which appears to be approximately normal--rotate your head 90 degrees clockwise, look at the "Tally" section of the distribution, and see if you agree), is:
Height Tally Frequency
59 II 2
60 IIIII 5
61 IIIIIII 7
62 IIIIIIIIII 10
63 IIIIIIIIIIIIIIII 16
64 IIIIIIIIIIIIIIIIIIIIII 22
65 IIIIIIIIIIIIIIIIIIII 20
66 IIIIIIIIIIIIIII 15
67 IIIIIIIII 9
68 IIIIII 6
69 IIIIII 6
70 III 3
71 I 1
72 I 1
___
123
Average heights of people in various countries
I thought you might find the following comparative data regarding average (mean) heights of adults to be of some interest. [I've tried to avoid the ' and " symbols in the text portion of this book, since they are confusable with apostrophes and quotation marks.] Note the greater average height for males in the Netherlands compared to males in the US. It wasn't always thus; Americans used to be taller than the Dutch. We (Americans) are actually getting shorter, primarily because of the immigration of Asians (see Bogin, 1998; Braus, 1993; Heubusch, 1997; McCook, 2001; Steckel, 1995; Usher, 1996).
| |USA |Germany |Japan |Netherlands |
|Males |175.5cm |174.5 |165.5 |182.5 |
| |5'9" 1/8 |5'8" 3/4 |5'5" 1/8 |5'11" 7/8 |
|Females |162.5 |163.5 |153.0 |169.6 |
| |5'4" |5'4" 1/4 |5'0" 1/4 |5'6" 3/8 |
Source: Statistics about Body Height website
That same source provided the following additional information for U.S. adult males and females:
|USA |Shortest |
|Males |person |
|5' 4" |James Madison |
|5' 6" |Benjamin Harrison |
| |Martin Van Buren |
|5' 7" |John Quincy Adams |
| |John Adams |
| |William McKinley |
|5' 8" |Ulysses S. Grant |
| |William H. Harrison |
| |James Polk |
| |Zachary Taylor |
|5' 8 1/2" |Rutherford Hayes |
|5' 9" |Millard Fillmore |
| |Harry S. Truman |
|5' 9 1/2" |Jimmy Carter |
|5' 10" |Calvin Coolidge |
| |Andrew Johnson |
| |Franklin Pierce |
| |Theodore Roosevelt |
|5' 10 1/2" |Dwight D. Eisenhower |
|5' 11" |Grover Cleveland |
| |Herbert Hoover |
| |Woodrow Wilson |
|5' 11 1/2" |Richard Nixon |
|6' 0" |James Buchanan |
| |Gerald R. Ford |
| |James Garfield |
| |Warren Harding |
| |John F. Kennedy |
| |James Monroe |
| |William H. Taft |
| |John Tyler |
|6' 1" |Andrew Jackson |
| |Ronald Reagan |
|6' 2" |Chester Arthur |
| |George H.W. Bush |
| |Franklin D. Roosevelt |
| |George Washington |
|6' 2 1/2" |Bill Clinton |
| |Thomas Jefferson |
|6' 3" |Lyndon B. Johnson |
|6' 4" |Abraham Lincoln |
Source: The Franklin Institute website
[Notes: 1. The current president (George W. Bush) is approximately 5ft 11in.
2. That frequency distribution of presidential heights is also not
displayed in the conventional manner, since there are names,
not frequencies, associated with each height, but I kinda like it.]
There has been considerable interest in the extent to which the relative heights of the candidates for the office of president of the United States might have affected the outcome of the election. Here are the data for the 20th century:
|Year |Winner |Height (inches) |Runner-Up |Height (inches) |
|1900 |McKinley |67 |Bryan |72 |
|1904 |T. |70 |Parker |72 |
| |Roosevelt | | | |
|1908 |Taft |72 |Bryan |72 |
|1912 |Wilson |71 |T. |70 |
| | | |Roosevelt | |
|1916 |Wilson |71 |Hughes |71 |
|1920 |Harding |72 |Cox |NA |
|1924 |Coolidge |70 |Davis |72 |
|1928 |Hoover |71 |Smith |NA |
|1932 |F. |74 |Hoover |71 |
| |Roosevelt | | | |
|1936 |F. |74 |Landon |68 |
| |Roosevelt | | | |
|1940 |F. |74 |Wilkie |73 |
| |Roosevelt | | | |
|1944 |F. |74 |Dewey |68 |
| |Roosevelt | | | |
|1948 |Truman |69 |Dewey |68 |
|1952 |Eisenhower |70.5 |Stevenson |70 |
|1956 |Eisenhower |70.5 |Stevenson |70 |
|1960 |Kennedy |72 |Nixon |71.5 |
|1964 |Johnson |75 |Goldwater |72 |
|1968 |Nixon |71.5 |Humphrey |71 |
|1972 |Nixon |71.5 |McGovern |73 |
|1976 |Carter |69.5 |Ford |72 |
|1980 |Reagan |73 |Carter |69.5 |
|1984 |Reagan |73" |Mondale |70 |
|1988 |G.H.W. Bush |74 |Dukakis |68 |
|1992 |Clinton |74 |G.H.W. Bush |74 |
|1996 |Clinton |74 |Dole |74 |
| | | | | |
NA = Not available
Source: Sommers (1996a), with the last two rows subsequently added
[Note: All of the heights for the winners in this table agree with those in the previous table, with the exception of Bill Clinton's (74 in vs. 74.5 in.]
The widely-held argument that the taller candidate in a presidential election is the more likely winner has been the topic of a great deal of controversy in the statistical literature. The well-known statistician William Kruskal (he of Kruskal-Wallis fame) argued that there was little or no good empirical evidence for such a claim, since the estimation of the heights of many of our former presidents is subject to considerable speculation (see Keyes, 1980 and Adams, 1994). More recently, Sommers (1996a, 1996b) carried out a statistical test (the related-samples "t" test) and found that the difference in mean height between the winning and the runner-up candidate was statistically significant, in favor of the winner. His work was roundly criticized by Ludwig (1997), however, since that test assumes random sampling and independence of the observations, both of which are violated by the data. (The measurements constitute an entire, albeit small, population, and some of the candidates' heights appear more than once in the data. FDR's height, for example, appears four times as a "winner", and some other candidates, e.g., Nixon, Carter, and the senior George Bush, appear twice each, since they were both "winners" and "losers"). Sommers (1997) replied by defending his test as having been carried out on a data set that "may be considered a random sample from an infinite conceptual population", a notion that is anathema to Ludwig [and to me]. Young and French (1998) and Sommers (2002) further argued that the taller presidents were the greater ones.
Other investigators (e.g., Gillis, 1982; McCann, 2001; Landsburg, 2002) have also gotten into the act in the controversy regarding the relationship between height and election outcome. All supported the claim that "taller usually wins".
CHAPTER 14: THE DISTRIBUTION OF WEIGHT
The frequency distribution of weight is said to be more platykurtic ("flatter") than the normal distribution, and with "fatter" tails [bad puns]. Wilcox and Russell (1983), however, found that the distribution of the birthweights of newborns is approximately normal.
NHANES III data (weights are in pounds)—see Appendix for NHANES IV data
Adult males: Percentiles
Ages: 5th 10th 15th 25th 50th 75th 85th 90th 95th
20-29 (n = 1630) 126.9 134.0 138.7 147.5 164.9 187.6 205.2 217.7 236.8
30-39 (n = 1481) 136.1 142.1 148.1 158.2 175.9 200.9 217.4 226.4 247.9
40-49 (n = 1226) 135.4 145.1 150.9 163.6 180.7 206.5 223.3 232.5 256.4
50-59 (n = 855) 139.6 150.1 158.4 166.7 184.7 206.8 221.6 231.5 251.3
60-69 (n = 1175) 134.5 141.9 148.8 160.1 181.1 203.3 216.4 224.4 236.2
70-79 (n = 875) 128.7 136.3 141.2 151.4 171.3 191.2 205.7 211.4 227.1
80+ (n = 700) 114.3 123.5 128.5 140.1 155.8 173.1 185.2 193.4 204.7
Note how the medians increase until age 50-59 and then decrease thereafter (rather dramatically), but once again that is attributable to different birth cohorts with different survival rates, not necessarily to loss of weight as men age, since these are cross-sectional, not longitudinal, data. And here's the distribution for males 40-49 displayed the "right" way:
Interval Frequency
256.4 61
___________________________________________
Total = 61+139+221+270+206+136+88+44+61 = 1226
Contrary to expectation, this distribution, like the distribution of height for these same 1226 males, also appears to be reasonably normal, albeit a bit skewed to the right with a longer right-hand tail. The same caution regarding the distribution of the heights for this age group--see previous chapter--applies here: choosing certain intervals rather than others can "force" normality.
Another note: The n's for the height distributions and the weight distributions for adult males should be the same for the same age groups (as they are for the 40-49 males), since all participants were supposed to be measured for both height and weight, but they're actually off by one here and there. No big deal, but it is annoying to have even a small amount of missing data in a project so carefully planned and carried out as NHANES III was.
Reference was made in the previous chapter to summaries of NHANES III height data for older Americans by Kuczmarski, Kuczmarski, and Najjar (2000). That same article also contains summaries of NHANES III weight data for older Americans. And for purposes of comparison with earlier data, here are some selected percentiles, in pounds, for White males aged 25-34 for NHANES I (n = 672):
5th percentile: 134
10th percentile: 142
25th percentile: 155
50th percentile (median): 173
75th percentile: 194
90th percentile: 217
95th percentile: 232
There has been considerable controversy regarding whether adult Americans are getting increasingly heavier (see the Body Mass Index section in Chapter 18). How do these data compare with the NHANES III data? Again, as for the heights, the age intervals are not quite the same and the weights of Black males are not reflected in the data just provided, but the median of 173 pounds for these NHANES I males is not very much different from an averaging of the median of 164.9 for ages 20-29 and the median of 175.9 for ages 30-39 in the NHANES III sample (see above).
Adult females: Percentiles
Ages: 5th 10th 15th 25th 50th 75th 85th 90th 95th
20-29 (n = 1665) 102.9 108.0 111.2 118.3 133.2 157.3 175.2 188.9 216.5
30-39 (n = 1775) 106.2 112.5 117.4 125.4 144.0 172.7 195.7 211.9 232.9
40-49 (n = 1368) 109.2 116.9 122.6 130.0 150.6 175.6 193.8 209.4 230.3
50-59 (n = 1006) 114.0 120.2 125.7 135.1 157.2 185.8 201.6 213.3 239.9
60-69 (n = 1172) 109.0 115.6 121.9 130.3 151.4 174.7 191.1 202.2 220.7
70-79 (n = 968) 100.5 110.5 116.3 125.0 142.4 166.8 180.6 189.5 213.8
80+ (n = 790) 92.0 100.0 105.4 114.1 131.4 149.4 159.1 168.7 186.3
[As expected, the weights for the women are uniformly lower than the weights for the men, with an increase in medians until age 50-59 and a serious decrease thereafter. There is a note to the table that reads: "Pregnant women are excluded." Makes sense. That may be one of the reasons why the n's for these weight distributions for adult females are smaller than the n's for the corresponding height distributions, especially for the 20-29 and 30-39 age groups.]
Males 3 mos.-19 years: Percentiles
Ages: 5th 10th 15th 25th 50th 75th 85th 90th 95th
3-5 mos. (n = 290) * 13.9 14.3 14.7 16.1 17.3 18.0 18.8 *
6-8 mos. (n = 320) * 16.3 16.8 17.5 19.1 20.8 22.0 22.8 *
9-11 mos. (n = 277) * 18.2 18.6 19.4 21.1 22.6 23.3 24.0 *
1 year (n = 663) 20.5 21.2 21.9 23.2 25.3 27.2 28.3 29.7 31.2
2 years (n = 644) 24.9 25.9 26.6 27.5 29.7 31.8 33.1 34.7 35.9
3 years (n = 516) 28.2 29.2 30.1 31.7 34.0 37.3 38.5 39.5 41.1
4 years (n = 549) 31.6 33.1 33.9 35.2 38.2 41.5 43.3 45.2 48.0
5 years (n = 497) 34.8 36.2 37.8 39.5 43.8 47.6 50.1 52.0 56.3
6 years (n = 283) * 40.3 41.4 43.3 48.2 54.5 59.4 65.3 *
7 years (n = 269) * 46.3 47.2 49.8 56.0 65.5 68.5 69.6 *
8 years (n = 266) * 51.0 52.7 55.1 61.4 72.9 81.7 93.0 *
9 years (n = 281) * 57.6 59.6 61.8 70.4 88.1 97.1 99.7 *
10 years (n = 297) * 61.3 62.7 69.6 79.5 91.1 107.0 109.0 *
11 years (n = 281) * 70.2 73.5 77.1 87.3 102.2 118.5 123.5 *
12 years (n = 203) * * 83.4 90.1 105.7 123.1 132.2 * *
13 years (n = 187) * * 90.5 98.2 115.2 134.4 145.7 * *
14 years (n = 188) * * 110.9 118.7 133.4 147.1 163.4 * *
15 years (n = 187) * * 114.3 121.1 139.8 170.4 184.0 * *
16 years (n = 194) * * 120.2 128.9 145.0 163.1 172.6 * *
17 years (n = 196) * * 132.1 137.7 153.9 173.7 186.5 * *
18 years (n = 176) * * 126.7 132.3 148.6 170.2 192.1 * *
19 years (n = 168) * * 133.2 139.8 157.1 169.0 191.1 * *
[I wonder why there's a decrease in the median from age 17 to age 18, followed by an increase from age 18 to age 19. And do you think the 170.4 and the 184.0 for the 15-year-old males are typos? They sure stand out (pardon the pun).]
Females 3 mos.-19 years: Percentiles
Ages: 5th 10th 15th 25th 50th 75th 85th 90th 95th
3-5 mos. (n = 308) * 12.4 12.9 13.3 14.6 16.2 16.9 17.4 *
6-8 mos. (n = 264) * * 15.8 16.4 17.4 19.0 19.9 * *
9-11 mos. (n = 315) * 17.1 17.5 18.0 19.6 21.2 22.2 22.9 *
1 year (n = 647) 19.6 20.1 20.8 21.7 23.4 25.9 27.3 28.2 29.4
2 years (n = 624) 23.7 24.5 25.0 26.3 28.7 31.2 32.7 33.9 35.8
3 years (n = 587) 27.3 28.7 29.5 30.8 33.3 36.1 38.1 39.1 41.9
4 years (n = 537) * 31.9 33.1 34.8 38.1 41.8 44.1 45.4 *
5 years (n = 554) * 35.2 36.4 38.6 43.3 47.7 51.8 54.1 *
6 years (n = 272) * * 40.7 42.4 46.2 53.4 60.4 * *
7 years (n = 274) * * 45.1 47.3 52.7 67.1 71.5 * *
8 years (n = 248) * * 51.5 53.8 62.7 72.8 77.8 * *
9 years (n = 280) * 54.8 57.6 61.6 69.5 82.0 97.7 104.2 *
10 years (n = 258) * * 64.1 66.9 79.1 96.0 108.1 * *
11 years (n = 275) * * 73.1 79.9 95.0 110.1 120.2 * *
12 years (n = 236) * * 80.0 91.0 102.5 123.3 132.8 * *
13 years (n = 220) * * 93.5 100.3 117.9 141.9 153.8 * *
14 years (n = 218) * * 104.2 110.3 118.9 148.1 155.4 * *
15 years (n = 191) * * 104.9 112.1 121.9 139.0 154.6 * *
16 years (n = 208) * * 111.6 115.6 123.8 145.9 157.1 * *
17 years (n = 201) * * 112.2 117.0 134.0 149.0 164.1 * *
18 years (n = 175) * * * 112.3 127.7 149.5 * * *
19 years (n = 177) * * * 117.7 133.5 145.0 * * *
[There are lots of missing data here, due to what they call not meeting their standard of reliability or precision, especially for the 18-year-old and 19-year-old women. And notice again the rather curious decrease in the median weight between age 17 and age 18, and subsequent increase at age 19.]
As they do for heights, the "Baby Bag" website provides average weights for boys and for girls in the 3 months to 13 years age range. And the website contains the following information:
Normal Weight for Boys:
A. Age 1 year: 21-32 lbs, mean: 10 kg (22 lb)
B. Age 2 years: 23-35 lbs, mean: 13 kg (28 lb)
C. Age 3 years: 27-39 lbs, mean: 15 kg (33 lb)
D. Age 4 years: 30-43 lbs, mean: 17 kg (37 lb)
E. Age 5 years: 34-52 lbs, mean: 19 kg (42 lb)
F. Age 6 years: 39-61 lbs, mean: 21 kg (46 lb)
G. Age 7 years: 43-70 lbs, mean: 23 kg (51 lb)
H. Age 8 years: 48-79 lbs, mean: 25 kg (55 lb)
I. Age 9 years: 53-90 lbs, mean: 28 kg (62 lb)
J. Age 10 years: 57-100 lbs, mean: 31 kg (68 lb)
K. Age 11 years: 62-112 lbs, mean: 35 kg (77 lb)
L. Age 12 years: 67-124 lbs, mean: 40 kg (88 lb)
M. Age 13 years: 72-138 lbs, mean: 45 kg (99 lb)
N. Age 14 years: 80-151 lbs, mean: 51 kg (112 lb)
O. Age 15 years: 91-162 lbs, mean: 57 kg (125 lb)
P. Age 16 years: 103-171 lbs, mean: 62 kg (136 lb)
Q. Age 17 years: 111-176 lbs, mean: 136 lbs
R. Age 18 years: 69 kg (152 lb)
[I don't know why there is only one weight given for 18-year-old boys. They did that for height also (see above).]
Normal Weight for Girls:
A. Birth: 5.8-9.4 lbs, mean: 3 kg (7 lb)
B. Age 1 year: 17-27 lbs, mean: 10 kg (22 lb)
C. Age 2 years: 22-34 lbs, mean: 12 kg (27 lb)
D. Age 3 years: 26-42 lbs, mean: 15 kg (32 lb)
E. Age 4 years: 29-48 lbs, mean: 16 kg (36 lb)
F. Age 5 years: 33-52 lbs, mean: 19 kg (41 lb)
G. Age 6 years: 37-59 lbs, mean: 21 kg (47 lb)
H. Age 7 years: 41-67 lbs, mean: 24 kg (52 lb)
I. Age 8 years: 45-79 lbs, mean: 26 kg (58 lb)
J. Age 9 years: 49-90 lbs, mean: 29 kg (64 lb)
K. Age 10 years: 53-102 lbs, mean: 32 kg (70 lb)
L. Age 11 years: 58-113 lbs, mean: 36 kg (79 lb)
M. Age 12 years: 64-128 lbs, mean: 40 kg (88 lb)
N. Age 13 years: 72-142 lbs, mean: 45 kg (99 lb)
O. Age 14 years: 83-151 lbs, mean: 49 kg (108 lb)
P. Age 15 years: 89-155 lbs, mean: 52 kg (114 lb)
Q. Age 16 years: 92-158 lbs, mean: 53 kg (117 lb)
R. Age 17 years: 94-160 lbs, mean: 54 kg (119 lb)
[The same two curiosities as for girls' heights: A range of normal weights at birth is provided for girls but not for boys; and no normal weight (not even a single weight) is provided for 18-year-old girls.]
The extremes
The heaviest adult was measured at 532 lbs in NHANES III; the lightest infant was measured at 6.2 lbs. In the 2001 BFRSS the heaviest self-reported weight for an adult was 776 lbs and the lightest self-reported weight was 50 lbs. (Again, both of those are hard to believe, aren't they?)
CHAPTER 15: THE RELATIONSHIP BETWEEN HEIGHT AND WEIGHT
From casual observation we know that many very tall people are also very heavy and many very short people are very light, but there are enough "tall and skinny" and "short and fat" people in the world so that the relationship between height and weight is far from perfect. Nevertheless, of particular interest to researchers is the form and the magnitude of that relationship, and the extent to which weight is predictable from height.
It is often assumed that weight varies with the square of height (which is the basis for the formula for body mass index--see Chapter 18), but McGee (2003) found that was rarely the case for the 25 data samples that he analyzed. [See also Heymsfield, Gallagher, et al. (2007).]
The data for many other samples indicate that the relationship is approximately linear and reasonably close to bivariate normal, despite the alleged platykurtosis [sounds like a disease, doesn't it?] of weight. Consider the following summaries of some investigations of the relationship between height and weight that have been carried out in the last several years:
NHANES III
Through the courtesy of the Inter-university Consortium for Political and Social Research (ICPSR) I was able to download the raw data for the Examination phase (Part 2) of NHANES III. [My thanks to Prof. Daniel McGee, Department of Statistics, Florida State University (personal communication, 11/26/03) for referring me to that valuable source.] The following scatterplots, associated descriptive statistics, and comments are based upon my own analyses of the relationship between height and weight for various subsamples of the NHANES III sample.
Here is the scatterplot of weight against height for the first 50 adult (age 20+) males in the NHANES III data set:
-
- *
300+
-
weight - *
-
-
240+ * *
-
- *
- * * * *
- * * * * * *
180+ * 2 * **2 *
- * * * * *
- *2 * * *
- ** * * ** *
- * *
120+ * ** *
- * *
------+---------+---------+---------+---------+---------
62.5 65.0 67.5 70.0 72.5 75.0
height
Correlation (Pearson product-moment) of height and weight = 0.540
The regression equation is
weight = - 304 + 7.00 height
[Notes:
1. The 2 indicates there are two approximately coincident data points in that region of the (X,Y) space.
2. The plot appears to be reasonably linear, but there is one rather serious "outlier" data point (height of about 71 inches and weight of over 300 pounds).
3. The correlation is moderate, though statistically significant.
4. Use of that regression equation to estimate adult male weight from adult male height would be better than nothing, but not very much better (see Chapter 6).]
5. These men are shorter than the men in the entire NHANES III sample, with a median height of 68.35 in vs. 69.1 in, and lighter, with a median weight of 169.7 lbs vs. 175.9 lbs--see the distributions in Chapter 3 and Chapter 4.]
Here is the scatterplot for the first 50 adult females:
240+ *
-
weight -
-
-
200+ *
- * * *
-
-
- * *
160+ * * * 2 *
- 2 **** *
- * * * * * *
- * * * 2 *
- ** * * * * * *
120+ * *
- * 2 **
- * *
- *
+---------+---------+---------+---------+---------+------
58.0 60.0 62.0 64.0 66.0 68.0
height
Correlation of height and weight = 0.325
The regression equation is
weight = - 96 + 3.76 height
[Notes:
1. Just as for the plot for adult males, the 2 indicates two approximately coincident data points.
2. This plot is also reasonably linear, but "fatter", and there is also one "outlier"
3. The correlation is even lower than for adult males, but still statistically significantly greater than zero.
4. The regression equation is different (naturally, because the means, standard deviations, etc. are different) and even less dependable than that for adult males.
5. In comparison with the adult females in the entire NHANES III sample, these women are of approximately the same height (median of 63.65 in vs. 63.7 in) and are about two pounds lighter (median of 142.7 lbs vs. 144.4 lbs).]
Controlling for age
It could be argued that both of the previous plots are not appropriate because they are confounded by age, i.e., they include data for men and women ranging in age from 20 to over 90. What is the relationship between height and weight within sex and age? Once again I turn to the NHANES III data for adult men of approximately the same age, in this case 40-49 (I didn't have the time or energy to do it for both sexes and for every age group). Here is the plot and its associated statistics:
-
400+ 2
-
weight -
-
- *
300+
- *
- *
- * * *
- 2
200+ * * * * ** * 2
- * * * * * *2 * ** ** *
- ** * 3 *3 ** *
- * *
- *
100+ *
-
-
+---------+---------+---------+---------+---------+------
62.5 65.0 67.5 70.0 72.5 75.0
height
Correlation of height and weight = 0.445
The regression equation is
weight = - 391 + 8.55 height
[Notes:
1. This time there are 2's and 3's, the former indicating two
approximately coincident data points, the latter indicating three.
2. The plot is a bit "flatter", there are two "outliers" with heights
of about 70 inches and weights of about 400 pounds (approximately
coincident with one another) than the plot for the 50 adult males of
varying ages, the correlation is a bit lower, and the regression
equation is different, but not as much different as I would have
expected.]
The previous three scatterplots for the NHANES III data are plots for
"unweighted observations" [no pun intended--"weight" has more than one
meaning]. NHANES actually employs a very complicated sampling design in
which each of the sampled observations is weighted in accordance with its
proportional representation in the U.S. population. Korn and Graubard (1998)
provide some guidelines regarding how to display scatterplots for differentially
weighted observations.
Controlling for almost nothing
Here is a scatterplot and some associated descriptive statistics for the heights
and weights of the first 50 participants in the BRFSS survey from the state of
Alabama (adults of both sexes and ages ranging from 18 to 74):
-
weight - *
-
-
250+ *
-
- * * *
- * *
- * * 2 *
200+ * * *
- * 2 2 7 *
- * 2 *
- * * * *
- * 2 * *
150+ * * *
- * * *
- * *
- *
-
--------+---------+---------+---------+---------+--------
59.5 63.0 66.5 70.0 73.5
height
Correlation of height and weight = 0.622
The regression equation is
weight = - 148 + 4.82 height
[Note:The correlation is higher than for any of the previous scatterplots (and would have been even higher if it weren't for a couple of outliers), primarily attributable to the inclusion on the same graph of the data for both sexes (38 males and 12 females) and secondarily attributable to the inclusion of all ages. Males are generally both taller and heavier than females, producing a longer and tighter scatterplot. The inclusion of persons of all ages should have a lesser influence, since height does not differ too much between younger and older adults (except for some elderly persons who have osteoporosis), and although weight does fluctuate considerably from age to age it does not do so monotonically. Sample size (n = 50 for all scatterplots) could of course be an additional factor. And although all of the BRFSS heights and weights were self-reported, the only way that should result in a higher correlation is if the shorter people over-estimate their heights and their weights and the taller people under-estimate their heights and their weights. Such has not been found to be the case--see the following chapter. ]
Minitab data
In the 1985 handbook and the 1986 manual for Version 5 of Minitab [my favorite version] there are directions for performing a variety of statistical analyses for data sets that came with that version of the program itself or for the researcher's own data. One of the Version 5 data sets is called "Pulse" and it consists of measurements on eight variables taken on a sample of 92 undergraduate students at Pennsylvania State University in the early 80s. Two of those variables are height and weight. When you plot the data for the two sexes separately (a wise thing to do), the scatterplot for the men (n = 57) is approximately linear and bivariate normal, although a bit fan-shaped (the Pearson r is .604); but the scatterplot for the women (n = 35) is more "buckshot" (with a Pearson r of .494). [Those results for the undergraduate students are remarkably similar to the results for the NHANES samples, aren't they?]
Wainer & Thissen data
Although Wainer and Thissen (1975) didn't identify the data as real or hypothetical, the correlation between height and weight for a group of 25 people was .83. When they reversed the height and weight measurements (65 inches and 128 pounds became 128 inches and 65 pounds) for one of those people [a dumb thing to do, but they were trying to make a point], thereby producing a serious "outlier" [try to visualize a person who is 128 inches tall and weighs 65 pounds], the correlation dropped to -.26!
The Heinz data
In their article published in the Journal of Statistics Education, Heinz, Peterson, et al. (2003) presented the results of the relationship between height and weight, and the relationships of several other body dimensions, for a sample of 507 physically active persons (247 males, 260 females). It is a “goldmine” of evidence regarding the prediction of weight from various measures of girth. For example, the correlation between height and weight was found to be “only” .717, with the best prediction of weight from height alone given by Weight (in kg) = -105 + 1.02 height (in cm). But if several measures of girth (all in cm) were incorporated [another bad pun], the multiple correlation was .986 and the regression (prediction) equation was:
Weight (in kg) = - 120 + 0.0781 Shoulder Girth + 0.198 Chest Girth
+ 0.340 Waist Girth + 0.0012 Navel Girth
+ 0.240 Hip Girth + 0.314 Thigh Girth + 0.0547 Flexed Bicep Girth
+ 0.532 Forearm Girth + 0.301 Knee Girth + 0.404 Calf Maximum Girth
- 0.0096 Ankle Minimum Girth - 0.118 Wrist Minimum Girth
+ 0.328 Height
[It turns out that even with such a high multiple correlation, the standard error of estimate (prediction) was approximately 2.2 kg (the person-to-person variability in weight was very high) and the making of all of those girth measurements may not be worth it, unless you have very good tape measures and no scales!]
Another data set
In their interesting article devoted to ways of trying to identify scientific fraud in the reporting of correlation coefficients (what they call "fabricated" correlations), Akhtar-Daneesh and Dehghan-Kooshkghazi (2003) provided a set of real height&weight data for 65 female students at Jahrom Medical School (in Iran). For those students the heights ranged from 145 cm (approx. 57 in) to 175 cm (approx. 69 in), with a mean of 159.5 and a standard deviation of 7.2; the weights ranged from 39 kg (approx. 86 lb) to 84 kg (approx. 185 lb), with a mean of 54.5 and a standard deviation of 9.2; and the correlation between height and weight was .43. Although these women were generally shorter and lighter than the adult females in the NHANES III sample, the correlation is very similar (.43 vs. .445).
[The authors gave the above information (ranges, means, standard deviations, correlations) to each of 34 faculty members at Jahrom Medical School and asked them to "guess" what raw heights and weights for an n of 65 would produce such correlations. The subsequently-computed correlations for those 34 data sets actually ranged from -.097 to +.996! (The authors provide a scatterplot for each data set; some of them are really bizarre!!)]
The relationship between the heights and the weights of identical twins
The methodological difficulties associated with an investigation of the relationship between the heights and the weights of identical (monozygotic) twins boggle my mind. You make all of the measurements and you create the data matrix. The first column contains the identifiers; the second column contains the heights; and the third column contains the weights. But there is a problem, starting with the first twin-pair. Where do you put the data? Is the entry in the first row, first column of the data matrix 1 (for twin-pair #1)? If so, what goes in the second column--both of their heights? If so, whose height is entered first? Likewise for the third column? Or is that entry in the first row, first column of the data matrix 1A, for twin A of twin-pair #1? If so, how do you determine who twin A is? Even if you can determine that (first out of the womb?) and you put his(her) height in column 2 and his(her) weight in column 3 [sounds like a Chinese menu], when you go to enter the data for twin 1a in the second row, something should bother you--the person in the second row is the twin of the person in the first row, not an "independent" person, so how can you indicate that, if and when it comes to creating a scatterplot of the data?
If my memory serves me correctly, in an international study several years ago the researchers tried to cope with this problem by plotting the weight of one member of each twin-pair (randomly chosen) against the height of the other member of each twin-pair. Creative, but dumb.
I also tried to cope with the problem (not very successfully) in an article I once wrote (Knapp, 1984), where I made the somewhat ludicrous suggestion of using different-colored data points in the scatterplot and/or to label the points in the scatterplot A for the first member and a for the second member of twin-pair #1; B for the first member and b for the second member of twin-pair #2; etc. (see above). Here are some real data for seven pairs of 16-year-old, Black, female, identical twins. What would you have done, dear reader (as Ann Landers used to say)?
Pair Height X (in inches) Weight Y (in pounds)
1 (Aa) A: 68 a: 67 A:148 a:137
2 (Bb) B: 65 b: 67 B:124 b:126
3 (Cc) C: 63 c: 63 C:118 c:126
4(Dd) D: 66 d: 64 D:131 d:120
5(Ee) E: 66 e: 65 E:123 e:124
6(Ff) F: 62 f: 63 F:119 f: 130
7(Gg) G: 66 g: 66 G:114 g:104
Source: Osborne (1980)
One possible solution is to forget about displaying the data in columns and in scatterplots, and to turn from Pearson's product-moment correlation coefficient to Fisher's (1958) intraclass correlation coefficient. (Fisher called Pearson's r an interclass correlation coefficient.) It is one of many examples of unit-of-analysis problems that plague much of scientific research; see, for example, Robinson (1950) and Knapp (1977). [The simpler term "unit-of-analysis" has recently been replaced by the more sophisticated term "hierarchical linear modeling"; see Raudenbush & Bryk (2002).]
Missing data
One of the most frustrating research experiences is to design a study with good measuring instruments and a defensible statistical analysis, only to discover that there are one or more pieces of missing data, due to an equipment breakdown, a subject's refusal to respond to a questionnaire item, a clerk's failure to record a measurement, or whatever. There are really only two ways to try to cope with such an eventuality: "deletion" or "imputation". For the deletion strategy, if there is a missing datum for any person you either delete that person entirely from all analyses (so-called "listwise" deletion), or delete that person from any analysis in which the variable with the missing datum is involved (so-called "pairwise" deletion). Listwise deletion and pairwise deletion are rarely appropriate, however, since they result in even more missing data!
For the imputation strategy, you try to estimate what the missing datum "might have been" and use that estimate in the analysis(es). Such estimation procedures range from the simple (but usually indefensible) substitution of the sample mean for the missing datum to the use of very complicated methods such as the expectation maximization (EM) algorithm. (See Little & Rubin, 2002 for the various advantages and disadvantages of those and other imputation techniques, but be forewarned that their textbook is very difficult reading. [Interesting aside: I once went to check the first edition of that book out of the library at The Ohio State University and I was told that it was missing!])
As far as investigating relationships between two variables such as height and weight are concerned, Korn and Graubard (1998) discussed how to indicate in a scatterplot which observations are actual and which have been imputed. Nice.
Changes and differences in heights and weights
Most of the studies summarized so far in this book have been concerned with analyses of height, weight, and their correlates at a single point in time (the study by Humphreys, Davey, & Park, 1985 on the relationship between height and intelligence is a notable exception). There have been a few investigations in which the emphasis was on how height and/or weight increased or decreased across time. One such study was carried out by Karpati, Rubin, et al. (2002), who provided data from the second and third cycles of the National Health Examination Survey (1963-1965 and 1966-1970) and NHANES III that suggested the rate of growth of boys at the earlier ages was greater in the latter study than in the earlier study. Another one was the work of Spencer (2002) who found on the basis of a summary of various previous investigations that the contribution of pubertal growth to adult height has been fairly constant for the last several years.
Heights, weights, and sizes
How do sizes of clothes relate to various heights and weights? I found the following information for women on Google Answers:
X-Small
Size 8
4'8" - 5'2"
90 - 120 lbs
Small
Size 10
5'0" - 5'4"
110 - 130 lbs
Medium
Size 12
5'0" - 5'9"
130 - 150 lbs
Large
Size 14
5'4" - 5'11"
140 - 160 lbs
X-Large
Size 16
5'6" - 6'0"
160 - 180 lbs
A puzzlement: One of the curious things about height and weight is how the two words are pronounced, given that each has six letters and the last five letters of both words are e, i, g, h, and t. "Height" is pronounced HYT and "weight" is pronounced WAYT. Why is that? Could it possibly be that if "height" were pronounced like "weight" is, it would sound just like "hate", and "hate" is not good? Or, is it because if "weight" were pronounced like "height" is, it would sound just like "white", and that would confuse everybody? As Casey Stengel used to say: "You can look it up." I tried, but without success. If you find out, please let me know.
CHAPTER 16: ESTIMATING HEIGHTS AND WEIGHTS
The estimation of heights has been the topic of many serious (and some not so serious) investigations. Two examples will be treated here in great detail. The first is Galton's classical data set for estimating sons' heights from fathers' heights, which is almost always referred to in any discussion of "regression toward the mean". The second example is the estimation of height from arm span and from self-reported height. And in the final sections I will try to summarize the results of several other studies of the validity of self-reported heights, self-reported weights, and other variables for estimating "actual" heights and weights.
The estimation of son's height from father's height
Francis Galton (1822-1911) was interested in how children resemble their parents. His disciple Karl Pearson (1857-1936) carried out a study in which he measured the heights of 1078 fathers and their sons at maturity. (See Galton, 1896; Pearson & Lee, 1903.) The data were:
|Family |Father's |Son's |
| |Height |Height |
|0001 | 68 | 69 |
|0002 | 72 | 72 |
|0003 | 69 | 71 |
|etc.. |... |... |
The relationship between father's height and son's height for the entire set of 1078 observations can best be revealed in the following scatterplot:
[pic]
There is a positive correlation between the heights of fathers and the heights of their sons. But the correlation is not perfect; some tall fathers have tall sons, others have sons of medium height, and a few have short sons. How predictable is son's height from father's height? If the father is 72 inches tall, for example, there is a great deal of variability in the heights of the sons. The average of the heights of the sons for these fathers is greater than the heights of the sons whose fathers are shorter than that, but it is less than 72 inches (from the scatterplot it appears to be about 71.5"); that is a demonstration of regression toward the mean.
Note: Although the scatterplot appears to be reasonably linear and bivariate normal, Wachsmuth, Wilkinson, and Dallal (2003) recently pointed out that there is a curious bend in the best-fitting "line" for that scatterplot and in some other scatterplots constructed by Galton and his colleagues. And for further insights regarding Galton’s height data see Hanley (2004).
The estimation of measured height from arm span and self-reported height
There is an interesting association between height and arm span that has been studied by many researchers. Most people are said to be approximately "square", i.e., their standing height is about the same as the distance between the tip of the middle finger of the left hand and the tip of the middle finger of the right hand when the arms are extended straight out to the sides. But there are some unusual, and often sad, exceptions, e.g., those people who suffer from Marfan's Syndrome, whereby their arm span is considerably greater than their height, the net effect of which is that their arms hang awkwardly low when they walk upright and they are exceedingly uncomfortable. (Some historians claim that Abraham Lincoln was a victim of Marfan's Syndrome.)
Because of this approximate "squareness", arm span measurement has been recommended as a surrogate measurement for stature, especially for those people who have difficulty standing up straight. (See, for example, Dwyer, Gallo, & Reichel, 1993; Jarvis, 1996; Lohman, Roche, & Martorell, 1988.) If the measurement of arm span also presents problems, self-reported height is sometimes resorted to. But how accurate are arm span and self-reported height as estimates of measured height?
Brown and her colleagues (Brown, Whittemore, & Knapp, 2000; Brown, Feng, & Knapp, 2002) have made extensive investigations of the estimation of height from both arm span and self-reported height. Here is a brief summary of some of their results:
Reliability of arm span: In the 2000 study, for a sample of 83 adults (26 men, 57 women), the correlation between the first and the second arm span measurements (an estimate of the reliability coefficient for the measured arm spans) was .998. In the 2002 study of 409 adults (188 men, 221 women) the measure/remeasure correlation was .997. Both of those are indicative of excellent reliability, but they are also a bit deceiving. The mean absolute difference in the 2000 study was approximately .30 cm.; in the 2002 study the mean absolute difference was approximately .53 cm. Those look like small numbers (less than a quarter of an inch). What they convey is that if we use those metal rules we're likely to be "off" from true height by less than 1/4 inch on the average. But that's "on the average"; we could be "off" by a lot less (that's the good news) or by a lot more (that's the bad news). The raw data (provided in Appendix A of Knapp, 2007 and available for downloading from my website, where that book is found) reveal that there were several differences of 0 inches between the two arm span measurements but there were also a few fairly large discrepancies --differences of an inch or more.
[In the 2002 study there were actually 82 different measurers (nursing students) using 82 different steel rules to measure the heights and the arm spans of their respective subjects. The one measurer whose measurements are perhaps the most suspect was Measurer # 57 who reported all measurements to the nearest half-inch and had no discrepancies whatsoever! The reliability coefficient for three other measurers (#37, 60, and 71) was also +1 and the mean absolute deviation was also 0 for arm span, so there could be some "hanky-panky" going on there. Some students involved in research studies have been known to try to "help out" the principal investigators by providing them with data they think the investigators want; others have been known to try to "louse up" the investigators.]
Validity of arm span: In the 2000 study the criterion-related validity coefficient was .933 (actually measured height was the criterion) and the mean absolute difference between arm span and height was 3.42 cm. In the 2002 study the validity coefficient was .900 and the mean absolute difference was 4.29 cm.
Reliability of self-reported height: No evidence; in the 2002 study they didn't ask the subjects to self-report their heights on two separate occasions (nobody other than Brener, McManus, et al., 2003--see below--has done that, as far as I can tell).
Validity of self-reported height: In the 2002 study, the validity coefficient was .970 and the mean absolute difference was 1.80 cm.
Conclusions: Both arm span and self-reported height appear to be reasonably accurate surrogates for actually-measured height, with self-report a bit better than arm span. Brown and her colleagues also derived regression equations for estimating measured height from arm span and/or from self-reported height, with and without the addition of other variables such as sex, age, and race, rather than merely using those surrogates singly.
Some other studies of arm span as a surrogate for height
Allen (1989): The principal result was that the mean arm span of the elderly women in the sample was approximately 5 cm greater than their mean height.
deLucia, Lemma, et al. (2002): In this study of four ethnic groups in Ethiopia (a total of 884 males and 822 females aged 18-50) the correlations between height and armspan ranged from .89 to .97.
Engstrom, Roche, and Mukherjee (1981): In their study of both boys and girls, the boys had greater arm span than height at all of the ages they studied (8 to 15), as did the older girls, but girls less than 11.5 years of age had greater height than arm span.
Kwok and Whitelaw (1991): They found arm span is a good predictor of height in the determination of body mass index (see Chapter 18), but men in their sample had greater differences between their arm spans and their heights than the women did.
Mitchell and Lipschitz (1982): Arm span was found to be an excellent surrogate for height in the determination of nutritional assessment, but on the average height was less than arm span for the older subjects.
Parker, Dillard, and Phillips (1996): Their results were similar to those of Allen (and of Mitchell & Lipschitz), but they found that arm span is a better predictor of height in Whites than in Blacks.
Steele and Mattox (1987): They also compared the predictability of height from arm span for Blacks and for Whites. The correlation was higher for Whites (.89) than for Blacks (.78).
[Notes regarding arm span:
1. The website claims that normal arm spans for children are 1 cm less than height; for adolescents arm span is the same length as height; for adults arm span exceeds height by more than 5 cm. The claim is also made that boys have longer arm spans than girls, and persons of African-American descent have longer arm spans than persons of other lineages. Unfortunately no evidence is provided to support those claims, and as is indicated in the summaries of the studies just considered, the evidence we do have is not that clear.
2. The alejandre/frisbie/math/leonardo website provides an interesting height vs. arm span exercise ("Leonardo daVinci Activity") for teachers of grades 6-8. The teachersource/mathline website has a similar exercise ("Reaching New Heights") for the same grades. There is also a reproduction on Ralph Larmann's University of Evansville website of a drawing that daVinci made of The Vitruvian Man. That same webpage contains Vitrovius' claim that a man's arm span is equal to his height. Some of his other claims can also be found on that webpage.]
Some other studies of self-reported height
The evidence regarding the validity of self-reported height is very extensive. The validity is usually assessed by comparing self-reported heights with measured heights, e.g., by the use of a stadiometer, a yardstick, or a tape measure. That is, those methods are taken to be the criteria for height measurement against which self-report must "measure up", so to speak. What follows is a brief summary of some of the many studies that have investigated the validity of self-reported heights of American men and women.
Brener, McManus, et al. (2003): Teenagers' self-reported heights (sample size = 2032) were on the average about 2.7 inches greater than their measured heights, which indicated that self-reported height was not a very valid measure for that sample. This was a consistent (reliable) finding, since there was very little difference (less than 1/4 in. on the average) between their self-report at Time 1 and their self-report at Time 2 (a day or two later). The correlation between self-reported height and measured height was .90.
Ezzati, M., Martin, H., et al. (2006). They obtained better estimates of the prevalence of obesity in the U.S. by correcting for bias in self-report, where men generally tend to over-estimate their heights. [See also their errata in the following issue, the letter to the editor by Gori, and the reply to Gori by Ezzati, Martin, et al. in a subsequent issue.]
Gunnell, Berney, et al. (2000): They found that both the elderly men (n = 118) and the elderly women (n = 139) in their study over-estimated their heights, the men by an average difference of 2.1 cm and the women by an average difference of 1.7 cm.
Hauck, White, et al. (1995): For their sample of 806 American Indian teenagers they found that overall both boys and girls over-estimated their heights.
Himes and Faricy (2001): Young children (less than 14 years of age) in NHANES III over-estimated their heights to such a degree that the authors recommended that self-reported height not be used as a surrogate for measured height for that age group.
Himes and Roche (1982): Wives (n = 100) over-estimated their own heights by about 1 centimeter on the average (and over-estimated their husbands' heights by about 1.3 centimeters on the average). The correlations between reported and measured heights were in the .84 to .97 range.
Imrhan, Imrhan, and Hart (1996): College students (n = 333 males and 136 females) self-reported their heights and were later actually measured. Some of them (245 males and 104 females) were told that they would be measured, but the others (88 males and 32 females) were not. Those who were informed beforehand that their heights would later be measured over-estimated their heights by an average of .67% (males) and .77% (females), and those who were not also over-estimated their heights by a lesser amount: .32% (males) and .25% (females). [Strange. I would have thought it would be the other way 'round.]
Kuczmarski, Kuczmarski, and Najjar (2001): For an NHANES III sample of 7772 men and 8801 women, they found that the discrepancy between self-reported height and measured height was significantly greater for the older subjects (the mean absolute error for height ranged from 2.92 to 4.50 cm for women and from 3.06 to 4.29 cm for men, 70 years and older).
Larson (2000): Both sexes (n = 19 males and 37 females) "over-reported" their heights--by between .38 cm and 2.1 cm on the average.
Nawaz, Chan, et al. (2001): In a small study of 97 overweight women they found that on the average the women over-estimated their heights.
Pirie, Jacobs, et al. (1981): Men (n = 1610) mostly over-reported their heights (especially the shorter men) and women (n = 1799) mostly under-reported theirs (especially the taller women).
Shaffer (1964): This early study is in a class all by itself. Children were asked to estimate their own heights and the heights of other persons who were important in their lives (mothers, fathers, teachers, etc.). Although there was no "gold standard" and Shaffer was not interested in the accuracy of their estimates, those estimates were found to be reliable, and she found some interesting relationships between the various estimates and selected personality variables.
Strauss (1999a): He analyzed the data for an NHANES III sample of 1657 adolescents, divided into various subgroups. The correlations between self-reported height and measured height ranged from .82 to .91. Over-all, actual height was under-estimated by approximately 1 cm.
Sullivan, Patch, et al. (1989): Different measurers who measured and re-measured the same elderly patients didn't agree very well with themselves or with one another; i.e., both the intra-measurer and inter-measurer reliabilities were low.
For an excellent summary of these and many other studies of the validity of self-reported heights (and weights--see the following section) in the U.S. and elsewhere, see Engstrom, Paterson, et al. (2003). They found that on the average women over-estimated their heights in 21 of the 26 self-reported height studies that they reviewed.
It is clear that in most studies people have been found to have a tendency to over-estimate their heights, for whatever reasons. Rowland (1990) and others have studied people's digit preferences when self-reporting their heights and weights. For some reason, certain people seem to prefer even-numbered to odd-numbered heights in numbers of inches. This is another example of what demographers call “heaping”.
Some studies of self-reported weight
Brener, McManus, et al. (2003): High school students (n = 2032) under-reported
their weights by about 3.5 pounds on the average. The correlation between
self-reported weight and measured weight was .93.
Ezzati, Martin, et al. (2006). They found that women generally under-estimated
their weights.
Gunnell, Berney, et al. (2000): The elderly males in their sample (n = 118) under-estimated their weights by 2.3 kg on the average, and the elderly females in their sample (n = 139) under-estimated their weights by 1.0 kg.
Hauck, White, et al. (1995): They found that overall the boys and the girls in their sample both under-estimated their weights.
Himes and Faricy (2001): Although there were many participants in the various age and sex subgroups who did not self-report their weights, for those who did the intraclass correlation coefficients between self-reported weights and measured weights ranged from .85 to .98. The weaker relationships were for the younger age groups.
Imrhan, Imrhan, and Hart (1996): The same 469 college students (see above summary for their self-reported heights) under-estimated their weights by .20% (informed males), .33% (informed females), .52% (uninformed males), and 2.10% (uninformed females).
Kuczmarski, Kuczmarski, and Najjar, M. (2001): Similar to the result for self-reported height, they found that the older subjects had greater discrepancies between their self-reported weights and their measured weights.
Larson (2000): The women (n = 37) under-estimated their weights, with the discrepancy between self-reported weight and measured weight greater for the heavier women.
Masheb and Grilo (2001): They were interested in self-reported weights by adults who suffered from binge eating disorder. They found that 73% of the 108 subjects estimated their weights within 5 pounds of their measured weights and 82% were within 10 pounds.
McCabe, McFarlane, et al. (2001) carried out a similar study, for 81 patients who were diagnosed with anorexia nervosa (AN) or with bulimia nervosa (BN). The AN group slightly over-estimated their measured weights whereas the BN group slightly under-estimated theirs.
Nawaz, Chan, et al. (2001): On the average, the 97 overweight women in their study under-estimated their weights; i.e., they self-reported weights that were lower than what they were subsequently measured to be.
Pirie, Jacobs, et al. (1981): They found that women (n = 1799) self-reported weights that were lower than their measured weights, as did heavy men; but men of lower weights self-reported weights that were higher than their measured weights (total n of males = 1610). About one-third of the participants of both sexes were "off" by five pounds or more. And they generally favored numbers ending in 0 or 5 for self-reported weights in pounds (the same "heaping" phenomenon as for heights--see above).
Rowland (1990). He also found the same “heaping” of weights on 0 and 5.
Strauss (1999a, 1999b): In the same study of 1657 adolescents referred to above in conjunction with self-reported height, self-reported weights and measured weights correlated .87 to .94 for the various sex and racial subgroups. Across the entire sample actual weights were under-estimated by approximately .4 kg. In another NHANES sample of 1932 adolescents he found that a high percentage of normal weight White girls considered themselves to be overweight even though they were not.
Villaneuva (2001): Using data for approximately 16,000 participants in NHANES III, they found that the discrepancy between self-reported weight and measured weight depended primarily upon sex. Overall, males over-estimated their weight by about .5 kg and females under-estimated their weight by about 1.5 kg.
As I indicated above with respect to self-reported height, Engstrom, Paterson, et al. (2003) summarized the results of several studies of self-reported weight. They found that in all 34 studies of self-reported weight that they reviewed (including several of those just listed), women under-estimated their weights, with the average discrepancy ranging from 0.20 kg to 3.54 kg.
Not surprisingly, there is a general tendency for both males and females to under-estimate their weight. (I say not surprisingly because in our culture it is much more acceptable to be skinny than to be fat. This matter will be treated in considerable detail in Chapter 17 and Chapter 18.)
The state-by-state self-reported weights in the BRFSS study have a seriousl "heaping" problem. In the first 50 observations for the state of Alabama, for example, 40 of the 50 weights ended in 0 or 5. And although the BRFSS study is the epitome of self-reported heights and weights, there is no way to determine whether or not those self-reports are accurate, since the participants were never actually measured.
Other studies of ways for estimating height and/or weight
BenAbdelkader, Cutler, and Davis (2002): Their very creative approach used stride length and "apparent height" from low-resolution videotapes of 45 subjects to provide a way of predicting measured height within 3.5 cm on the average. "Apparent height" is a person's relative height (while walking) as compared with the background from the video image.
Bermudez, Becker, and Tucker, (1999): The published regression equations for predicting standing height from knee height were found to over-estimate the standing height of a group of 569 Hispanic subjects (ages 60-92) living in the northeastern United States. It was apparently a reaction to the work of Chumlea, Guo, et al. (see following reference).
Chumlea, Guo, et al. (1998): In this study published a year earlier the researchers derived regression equations for estimating stature from knee height, sitting height, and age for various sex-by-ethnicity subgroups in NHANES III (total n = 4750) and found such equations to provide accurate surrogates for measured height.
Feldesman and Fountain (1998): Their study was concerned with the estimation of height from femur length. They showed that the femur-to-stature ratio varied considerably across various racial subgroups, and they derived a regression equation for predicting height from both femur length and race.
Geraghty and Boone (2003). This fascinating study of height estimation, weight estimation, body mass index (BMI) estimation, and body surface area (BSA) estimation using abdominal computed tomography (CT) for a sample of 87 adult subjects (51 men, 36 women) produced the following results for height and weight: Correlation between CT estimates and actual heights = .662 (men) and .656 (women); mean absolute difference = 9.9 cm (men) and 6.2 cm (women). Correlation between CT estimates and actual weights = .956 (men) and .932 (women); mean absolute difference = 4.819 kg (men) and 5.277 kg (women).
Gonzalez, J. (2003). The principal finding was that listeners were not very good at estimating speakers' heights or weights from merely hearing their voices (only 14% of the estimates were sufficiently close), despite the findings of Lass and Davis (1976), Lass, Andes, et al. (1982), and others to the contrary.
Gunnell, Berney, et al. (2000). Leg length and height correlated about .70 with standing height for both men and women. Therefore leg length was not a very good predictor of height.
Hensley (1998): In an interesting twist, Hensley asked 59 college students (25 males and 34 females) to self-report their desired heights in addition to their perceptions of their own heights (see above for the latter). The desired heights correlated .97 (males) and .98 (females) with actual heights; the mean absolute differences were .06 in (males) and .02 in (females)--remarkably close to their measured heights.
Hickson and Frost (2003): For their sample of elderly patients they found that despite high correlations with standing height (.86 and .89), on the average demi-span over-estimated standing height by 4.33 cm on the average and knee height under-estimated by .6 cm.
Jensen, Friedmann, et al. (2003): For 213 patients who had documented weights in their nursing records, 55 of them had actual weights which differed from the documented weights by 5 pounds or more.
Maynard, Galuska, et al. (2003): The principal finding of this study, another investigation based upon NHANES III data (n = 5500), was that 32.1% of mothers of overweight children claimed that those children were "about the right weight".
Pressman, Bienstock, et al. (2000): They found that prediction of birth weight by ultrasound in the third trimester was no better, and was actually a bit worse, than the prediction in the second trimester (mean absolute discrepancy of 197 g vs. 235 g).
Reed and Price (1998). Estimates of heights and weights by family members correlated highly with actually measured heights and weights (.95 and .94, respectively), but on average the height estimates were over-estimates and the weight estimates were under-estimates (by 1.4 cm and 4.1 kg, respectively).
Rogerson, Gallagher, and Beebee (2000): Their research was concerned with a double estimation problem--using a tape measure instead of calipers to measure knee height and then using that measurement to estimate standing height. For a sample of 56 clients with developmental disabilities, they found that the tape measurements consistently over-estimated knee height, which in turn consistently over-estimated standing height.
Watt, Pickering, and Wales (1998): Fourteen children had their heights measured by two measurers using an ultrasonic experimental stadiometer ("Gulliver") and a traditional mechanical stadiometer (the "gold standard"). The "Gulliver" under-estimated their heights by 2.8 cm on the average, and was also not found to be very reliable.
Jesus' height
One of the interesting examples of heights is that of Jesus Christ (see, for example, Harris, 1926; Craveri, 1967). Some authors and some artists have portrayed him as very tall; others as of average or even below average height compared to the men of his time. As you might imagine, it is very difficult to determine just how tall he was [stadiometers hadn't yet been invented!], and the matter of his height has been a topic of considerable controversy in the religious literature. (For more discussion of Jesus' height and what he may have looked like, see the website and the Google Answers posting regarding the questions "How tall was Jesus Christ?" and "Who was the tallest desiple [sic!]?")
[A person in the bible whose height has also been the subject of some controversy is Goliath, the "giant" who was alleged to have been felled and slain by a single stone hurled by David. His height was said to be "six cubits and a span" (1 Samuel 17:4). There are at least two definitions of a "cubit"--12 inches and 20 inches. (A "span" is 9 inches.) Using the former definition, Goliath was 6ft 9in; using the latter definition, he was 10ft 9in. (See the comments by John P. Boatwright on the "How long is a cubit?" webpage and similar comments on the One Name Left website. The latter source also suggests that Goliath may have suffered from acromegaly, a disorder caused by the secretion of too much growth hormone.)]
The heights of historical populations
There is an entire specialization called “historical anthropometrics” (see Cuff, 2004), which is devoted to the analysis of height and other anthropometric variables as indicative of the health, nutrition, and well-being of various cultures and nations. Of particular interest to demographers, economists, and others is the estimation of the distributions of the heights of populations of people who lived many years ago by appealing to the available data of certain samples of those populations, e.g., military recruits, whose heights were actually measured. One of the most extensive studies of such samples was carried out by Wachter and Trussell (1982). They concentrated on estimating the lower "tail" of the population distributions, assuming that shorter people were not sufficiently represented in the military samples because of minimum height regulations. Other researchers, e.g., Komlos (no date) cautioned that such estimates of "deficient height samples" are fraught with methodological difficulties.
Near the beginning of their article, Wachter and Trussell cited Abraham, Johnson, and Najjar (1979) regarding height and weight data from NHANES I (the first National Health and Nutrition Examination Survey). They (Wachter and Trussell) were concerned about the normality assumption for the population distributions that they were attempting to estimate, so they tested that assumption for the height distribution of the White males aged 25-34 in the NHANES I sample. They found the distribution to be very close to normal. [Take a look at the percentiles provided for that distribution in Chapter 13, and use your knowledge of the normal distribution to see if you agree.]
Forensic estimates of heights and weights
Forensic scientists are just as interested in the heights and the weights of corpses as the rest of us are interested in the heights and weights of live bodies. One of the principal reasons for that is to assist in the identification of human remains. Here are summaries of a few of their studies:
Robbins (1986) discussed a formula derived by Topinard in the mid-1800s for estimating heights from footprints made by the later-deceased (foot length divided by .15). He (Robbins) derived comparable formulas for estimating both height and weight from footprints.
Giles and Vallandingham (1991) also reviewed the forensic literature on estimating height from footprints, and they provided some additional data from U.S. Army records that might improve such estimates.
Giles and Hutchinson (1991) reported that adults over age 45 over-estimated their heights to such an extent that using those estimates (for example, heights as indicated on drivers' licenses) as surrogates for measured heights is not advisable for identifying skeletal remains.
The "bottom line" regarding the estimation of height and weight
If you can't use a stadiometer to measure the heights of adults and you need to estimate them, you usually can't go too far wrong in asking the adults to self-report their heights and using a regression equation to predict their measured heights. (Using a self-reported height all by itself it is not a good idea, because it may be a serious under-estimate or over-estimate of actual height.) The next best thing would seem to be to measure arm span and again use a regression equation to predict standing height. Knee height is not a very good predictor of stature, nor is abdominal computed tomography. You probably don't want to ask the subjects' family members and friends for their estimates of the subjects' heights, but you may want to ask the subjects for their desired heights and use the desired heights instead of, or in addition to, their perceptions of their own heights.
As far as weight is concerned, self-reports are almost always under-estimates, so some correction would need to be made if self-reported weights are to be used to estimate actual weights. Abdominal computed tomography is much better for weight than it is for height. Again, don't ask family members or friends to estimate subjects' weights.
CHAPTER 17: "IDEAL” WEIGHT
For many years there was considerable interest in the concept of "ideal" weight. I (Knapp, 1983), along with many others (e.g., Gaesser, 2002), have been very critical of that concept, which was originally based upon mortality tables developed for the life insurance industry (see below).
There are also some mathematical equations for ideal weight that have been proposed. Consider, for example, the following equations that can be found on the website [I have also included their equation for predicted weight (see previous chapter)]:
I. Calculation: Male Ideal Weight in Kg
A. Weight = 50 + 2.3 x (height in inches - 60)
B. Weight = 50 + 0.91 x (height in centimeters - 152.4)
II. Calculations: Female Ideal Weight in Kg
A. Weight = 45 + 2.3 x (height in inches - 60)
B. Weight = 45.5 + 0.91 x (height in centimeters - 152.4)
III. Approximate predicted weight estimate
A. Male: 106 + (height in inches over 60) x 6
B. Female: 100 + (height in inches over 60) x 5
Pai and Paloucek (2000) discussed the origins of such equations. Kamel and McNeill (2002) derived one of them. And Dr. Steven Halls' website (halls.md) provides some additional information about ideal weight and how to determine it.
More recently the concept of "ideal" weight has been replaced by the concept of "desirable" weight based upon the body mass index (BMI), developed by Quetelet, which is defined as weight in kilograms divided by the square of height in meters (see the following chapter).
The first tables of "ideal weight" for adults were produced in 1959 by the Metropolitan Life Insurance Company, and were structured according to sex and "frame size" [a wrist circumference measurement that was never actually taken in the studies upon which the tables were based--see Knapp (1983) and Gaesser (2002)--but which can be measured in a variety of ways (Novascone & Smith, 1989)]. They were revised in 1983. Both tables are reproduced here, for comparison purposes:
|Ages 25-59, Weight in LBS (weight in KGS), without shoes or clothing |
|1959 Men/ *1983 Men |
|Height |Small Frame |Medium Frame |Large Frame |
|5'1'' |106-114 |112-123 |120-135 |
|*5'1'' |123-129 (55.9-58.6) |126-136 (57.3-61.8) |133-145 (60.5-65.9) |
|5'2" |109-117 |115-127 |123-138 |
|*5'2" |125-131 (56.8-59.5) |128-138 (58.2-62.7) |135-148 (61.4-67.3) |
|5'3" |112-120 |118-130 |126-142 |
|*5'3" |127-133 (57.7-60.5) |130-140 (59.1-63.6) |137-151 (62.3-68.7) |
|5'4" |115-123 |121-133 |129-146 |
|*5'4" |129-135 (58.6-61.4) |132-143 (60.0-65.0) |139-155 (63.2-70.5) |
|5'5" |118-127 |124-137 |132-150 |
|*5'5" |131-137 (59.5-62.3) |134-146 (60.9-66.4) |141-159 (64.1-72.3 |
|5'6" |122-131 |128-141 |136-155 |
|*5'6" |133-140 (60.5-63.6) |137-149 (62.3-67.7) |144-163 (65.5-74.1) |
|5'7" |126-135 |132-146 |141-160 |
|*5'7" |135-143 (61.4-65.0) |140-152 (63.6-69.1) |147-167 (66.8-75.9) |
|5'8" |130-139 |136-150 |145-164 |
|*5'8" |137-146 (62.3-66.4) |143-155 (65.0-70.5) |150-171 (68.2-77.7) |
|5'9" |134-144 |140-154 |149-168 |
|*5'9" |139-149 (63.2-67.7) |146-158 (66.4-71.8) |153-175 (69.5-79.5) |
|5'10" |138-148 |144-159 |153-173 |
|*5'10" |141-152 (64.1-69.0) |149-161 (67.7-73.1) |156-179 (70.9-81.4) |
|5'11" |142-156 |148-164 |158-178 |
|*5'11" |144-155 (65.4-71.4) |152-165 (69.1-75.0) |159-183 (72.3-83.2) |
|6'0" |146-156 |152-169 |162-183 |
|*6'0' |147-159 (66.8-73.2) |155-169 (70.5-76.8) |163-187 (74.1-85.0) |
|6'1" |150-161 |156-174 |167-188 |
|*6'1" |150-163 (68.2-74.1) |159-173 (72.3-78.6) |167-192 (75.9-87.3) |
|6'2" |154-165 |161-179 |172-193 |
|*6'2" |153-167 (69.5-75.9) |163-177 (74.1-80.5) |171-197 (77.7-89.5) |
|6'3" |158-169 |166-184 |176-198 |
|*6'3" |157-172 (71.4-78.2) |167-182 (75.9-82.7) |176-202 (80.0-91.8) |
|Ages 25-59, Weight in LBS (weight in KGS), without shoes or clothing |
|1959 Women/ *1983 Women |
|Height |Small Frame |Medium Frame |Large Frame |
|4'8" |89-95 |93-104 |101-116 |
|4'9" |91-98 |95-107 |103-119 |
|*4'9" |99-108 (45.0-49.1) |106-118 (48.2-53.6) |115-128 (52.3-58.2) |
|4'10" |93-101 |98-110 |106-122 |
|*4'10" |100-110 (45.5-50.0) |108-120 (49.1-54.5) |117-131 (53.2-59.5) |
|4'11" |96-104 |101-113 |109-125 |
|*4'11" |101-112 (45.9-50.9) |110-123 (50.0-55.9) |119-134 (54.1-60.9) |
|5'0" |99-107 |104-116 |112-128 |
|*5'0" |103-115 (46.8-52.3) |112-126 (50.9-57.3) |122-137 (55.5-62.3) |
|5'1" |102-110 |107-119 |115-131 |
|*5'1" |105-118 (47.7-53.6) |115-129 (52.3-58.6) |125-140 (56.8-63.6) |
|5'2" |105-113 |110-123 |118-135 |
|*5'2" |108-121 (49.1-55.0) |118-132 (53.6-60.0) |128-143 (58.2-65.0) |
|5'3" |108-116 |113-127 |122-139 |
|*5'3" |111-124 (50..5-56.4) |121-135 (55.0-61.4) |131-147 (59.5-66.8) |
|5'4" |111-120 |117-132 |126-143 |
|*5'4" |114-127 (51.8-57.7) |124-138 (56.4-62.7) |134-151 (60.9-68.6) |
|5'5" |115-124 |121-136 |130-147 |
|*5'5" |117-130 (53.2-59.1) |127-141 (57.7-64.1) |137-155 (62.3-70.5) |
|5'6" |119-128 |125-140 |134-151 |
|*5'6" |120-133 (54.5-60.5) |130-144 (59.1-65.5) |140-159 (63.6-72.6) |
|5'7" |123-132 |129-144 |138-155 |
|*5'7" |123-136 (55.9-61.8) |133-147 (60.5-66.8) |143-163 (65.0-74.1) |
|5'8" |127-136 |133-148 |142-160 |
|*5'8" |126-139 (57.3-63.2) |136-150 (61.8-68.2) |146-167 (66.4-75.9) |
|5'9" |131-140 |137-152 |146-165 |
|*5'9" |129-142 (58.6-64.5) |139-153 (63.2-69.5) |149-170 (67.7-77.2) |
|5'10" |135-144 |141-156 |150-170 |
|*5'10" |132-145 (60.0-65.9) |142-156 (64.5-70.9) |152-172 (69.1-78.6) |
|*5'11" |135-148 (61.3-67.3) |145-159 (65.9-72.3) |155-176 (70.5-80.0) |
Ellen Goodman once wrote that if she were 5ft 10in tall her present weight would be ideal, but that she unfortunately was only 5ft 8in. She said that the solution to her problem was to gain height, not to lose weight. Andy Rooney said that he should be 6ft 6in because he weighs approximately 205 pounds; he, like Ellen Goodman, is 5ft 8in.
Some sources (e.g., Heiat, Vaccarino, & Krumholz, 2001; Heiat, 2003) claim that the Metropolitan charts and their BMI counterparts are not appropriate for elderly people. The Today's Seniors website, for example, recommends the use of the following chart for senior citizens who are concerned about their "ideal" weights:
|Height |Weight |
|feet / inches |in Pounds |
| | |
|4' 8" |84 - 124 |
|4' 9" |87 - 129 |
|4' 10" |90 - 133 |
|4' 11" |93 - 138 |
|5' 0" |96 - 143 |
| | |
|5' 1" |99 - 147 |
|5' 2" |102 - 152 |
|5' 3" |106 - 157 |
|5' 4" |109 - 162 |
| | |
|5' 5" |113 - 167 |
|5' 6" |116 - 172 |
|5' 7" |120 - 178 |
|5' 8" |123 - 183 |
| | |
|5' 9" |127 - 188 |
|5' 10" |130 - 194 |
|5' 11" |134 - 200 |
|6' 0" |138 - 205 |
| | |
|6' 1" |142 - 211 |
|6' 2" |146 - 216 |
|6' 3" |150 - 222 |
|6' 4" |154 - 229 |
| | |
|6' 5" |158 - 235 |
|6' 6" |162 - 241 |
|6' 7" |166 - 247 |
|6' 8" |170 - 254 |
[I think those weight ranges are a bit too wide (another terrible pun), don't you? And although it is commendable that they are not broken down by "frame size", I would have thought that there would be separate charts for men and for women.]
Weight standards
Closely associated with the concept of "ideal" weight is the notion of weight "standards" for certain occupations. The United States Army, for example, has the following maximum weight requirements for males and for females of the indicated heights (I have also included the notes regarding the taking of the height and weight measurements):
Notes:
1. The height will be measured in stocking feet (without shoes), standing on a flat surface with the chin parallel to the floor. The body should be straight but not rigid, similar to the position of attention. The measurement will be rounded to the nearest inch with the following guidelines:
a. If the height fraction is less than 1/2 inch, round down to the nearest whole number in inches.
b. If the height fraction is 1/2 inch or greater, round up to the next highest whole number in inches.
2. The weight should be measured and recorded to the nearest pound within the following guidelines:
a. If the weight fraction is less than 1/2 pound, round down to the nearest pound.
b. If the weight fraction is 1/2 pound or greater, round up to the nearest pound.
3. All measurement will be in a standard PT uniform (gym shorts and T-shirt, without shoes).
4. If the circumstances preclude weighing soldiers during the APFT, they should be weighed within 30 days of the APFT.
5. Add 6 pounds per inch for males over 80 inches and 5 pounds for females for each inch over 80 inches.
Information Courtesy of U.S. Army
A few observations on my part:
1. These maximum weights commendably take age into account, but the variation across the various age levels seems too regular. Some "smoothing" must be going on.
2. The maximum weight for an age 40+ male who is 69 in tall (the approximately "average" adult U.S. male) is considerably greater than the upper limit of the "ideal" weight for an adult male in the 1983 Metropolitan charts given above (186 lbs vs. 173 lbs), whereas the maximum weight for an age 40+ female who is 64 in tall (the approximately "average" adult female) is somewhat less than the upper limit of the "ideal" weight for an adult female in the 1983 Metropolitan charts (145 lbs vs. 151 lbs).
3. I have no idea what the basis (if any) for that fifth note is!]
Johnson (1997) gave an interesting account of how the Army weight standards evolved. And Nolte, Franckowiak, et al. (2002) used the NHANES III data to provide the following information regarding estimates of the percentage of males and females who are 17-20 years of age and whose weight exceeds the Army maximums (they also provided similar information for the Navy, Air Force, and Marines):
Group n Percentage (95% confidence interval)
Total Men 695 18 (13-23)
Non-Hispanic White Men 167 20 (11-27)
Non-Hispanic Black Men 229 19 (14-26)
Mexican-American Men 268 24 (17-33)
Total Women 780 43 (37-49)
Non-Hispanic White Women 217 36 (30-45)
Non-Hispanic Black Women 270 56 (47-62)
Mexican-American Women 250 55 (47-65)
[The moral to the story? Either get young adults 17-20 years of age, especially women, to reduce their weights, or change the weight standards. Otherwise there will not be much of a recruiting pool to choose from.]
CHAPTER 18: BMI, BSA, BIA, and BMR
I like to think of this chapter as the "B" chapter. In it I discuss a number of terms that have relevance to height and weight, all of which start with the letter B, and all of which have three-letter abbreviations. They are:
Body Mass Index (BMI)
Body Surface Area (BSA)
Bioelectrical Impedance Analysis (BIA)
Basal Metabolic Rate (BMR)
BMI
BMI has already been defined in the previous chapter: weight in kilograms divided by the square of height in meters (1 meter = 100 centimeters). It can also be calculated by dividing weight in pounds by the square of height in inches and multiplying by 703.1. BMI is now the most common method for determining desirable weight-for-height and for defining obesity (serious overweight) and protein energy malnutrition (serious underweight). The National Institutes of Health provide the following guidelines regarding BMI (se also the definitions and comments provided at the National Center for Chronic Disease Prevention and Health Promotion's website):
• Underweight = 85%): 22
3. Overweight BMI (>95%): 25
D. Age 14
1. Mean BMI (50%): 19
2. At Risk BMI (>85%): 23
3. Overweight BMI (>95%): 27
E. Age 16
1. Mean BMI (50%): 20
2. At Risk BMI (>85%): 25
3. Overweight BMI (>95%): 29
Interpretation: Girls (Derived from CDC BMI charts)
A. Approximation
1. Overweight BMI = (Age in years) + 13
B. Age 10
1. Mean BMI (50%): 17
2. At Risk BMI (>85%): 20
3. Overweight BMI (>95%): 23
C. Age 12
1. Mean BMI (50%): 18
2. At Risk BMI (>85%): 22
3. Overweight BMI (>95%): 26
D. Age 14
1. Mean BMI (50%): 19
2. At Risk BMI (>85%): 24
3. Overweight BMI (>95%): 28
E. Age 16
1. Mean BMI (50%): 20
2. At Risk BMI (>85%): 25
3. Overweight BMI (>95%): 29
[Notes: They rounded the 703.1 to 700. WHO is the acronym for World Health Organization. And several of the interpretations are subject to differences of opinion. For example, 20-22 is a very narrow "ideal weight" range; and claiming that BMIs less than 25 are "at risk" (for obesity) strikes me as overly pessimistic.]
Here are some interesting state-by-state data regarding BMI taken from Table 2 of the article by Mokdad, Ford, et al. (2003)--see also the article by Mokdad, Bowman, et al. (2001). The data were obtained for a subsample of 195005 of the 212510 adults aged 18 years or older who participated in the 2001 BRFSS survey that has been referred to in four of the previous chapters (3, 4, 5, and 6) of this book. The SE's are the standard errors of the percentages--the "margins of error" for the sample percentages. See Chapter 20 for more information about the association between obesity and diabetes.
[A couple of observations regarding that table:
1. Colorado has the smallest percentage of obese adults (14.4) and Mississippi has the largest percentage of obese adults (25.9). (Keep in mind that the data come from self-reports and the actual percentages are probably higher, since most people have a tendency to under-estimate their weights--see Chapter 16.) Why is that? I haven't got the slightest idea. Have you?
2. The sample sizes for the states range from a low of 1888 for the District of Columbia to a high of 8628 for Massachusetts. Sample size and sample percentage both influence the accuracy of the estimates. For example, the standard error associated with Nevada's obesity percentage is the largest of all of the states (1.35), and the percentage of obese adults in the entire population of the state of Nevada could easily be as small as 16.4 or as large as 21.8 (the approximate 95% confidence interval around the sample percentage of 19.1).]
There is considerable controversy regarding whether or not Americans are in general too heavy. Dortch (1997), for example, claimed that the percentage of overweight people in the U.S. was increasing steadily, and she provided some interesting statistics as evidence. Gaesser (2002) did not deny such evidence, but he argued that the so-called "obesity epidemic" is over-blown (I can't seem to avoid these terrible puns), and the real problem is diet and lack of exercise, not obesity per se. He cited the work of McGinnis and Foege (1993, 1998), which he believes to have been mis-interpreted as a basis for the "obesity epidemic", since they identified "Diet and activity" as the second greatest "actual" cause of death (tobacco being the first), not overweight or obesity. [In two of the most recent articles on the topic, Manson & Bassuk (2003) and Manson, Skerrett, et al. (2004) refer to obesity as "pandemic", which I take to be worse than "epidemic". See also the chapter by Manson, Skerrett, & Willett (in press).]
Most of the claims and counter-claims regarding the prevalence of obesity are based upon BMI, about which much has been written in the last 25 years or so. What follows are brief summaries of some of such writings. The "effects" of overweight and obesity will be treated in Chapter 20. [For more than you ever wanted to know about obesity, read the book entitled Fat, by Robert Pool (2001), the same person who wrote Eve’s rib, which I cited earlier in the chapter on sex differences. And you may also want to take a look at the article by Christakis and Fowler (2007), who claim that tendency to obesity can and has spread (another bad pun) from some members of social networks to other members!]
The supplement to the March, 1998 issue of Pediatrics was entitled "The causes and consequences of obesity in children and adolescents". One of the articles contained in that supplement was directly concerned with BMI. It was written by Troiano and Flegal (1998); they reported that the prevalence of overweight BMI for those age groups was approximately 11%, with the greatest increase coming between NHANES II and NHANES III (roughly 1988 to 1994).
Supplement 2 to the March 1999 issue of the International Journal of Obesity contained several papers that had been presented at a 1997 conference in Minnesota entitled "Childhood and Adolescent Obesity: Prevention and Treatment". Four of those articles were concerned with BMI.
1. Himes (1999): He compared six different indicators of obesity (BMI, triceps skinfolds, subscapular skinfolds, the sum of four skinfolds, waist circumference, and percentage of body fat) for a sample of 625 White 12-18-year-olds in NHANES III, with respect to identifying the heaviest persons in that age range. He found the agreement to be moderate and he argued for a standardized definition of youth obesity.
2. Luepker (1999): Although her paper was concerned primarily with programs for increasing physical activity, she reported that between 1986 and 1996 there were significant increases in average BMI for all subgroups of Minnesota teenagers aged 10-14 (boys, girls; Blacks, Whites; etc.).
3. Troiano and Flegal (1999): Like Himes, they were concerned with various overweight indicators, and using NHANES data they found that the various estimates of overweight prevalence (including those based upon BMI percentiles) ranged from 11% to 22% for children (6-11 years of age) and from 11% to 24% for adolescents (12-17 years of age).
4. Zephier, Himes, and Story (1999): They studied a sample of 12559 American Indian children aged 5-17. Using definitions of >85th percentile (for the U.S. as a whole) of BMI for overweight and >95th percentile for obesity, 39.1% of the males and 38.0% of the females were found to be overweight; of those, 22.0% of the males and 18.0% of the females were obese.
In addition to the Troiano and Flegal (1998) and Troiano and Flegal (1999) studies cited above, Flegal, the Kuczmarskis, Ogden, Troiano, and their colleagues have carried out a number of other studies that are concerned with BMI. The results of some of those studies are:
a. Prevalence of overweight for adults 20-74 years of age increased from 25.4% in NHANES II (mean BMI = 25.3) to 33.0% in NHANES III (mean BMI = 26.2). (Flegal, 1996).
b. Overweight prevalence in a particular age group may be over-estimated by as much as three percentage points depending upon the cut-off points used for the various age groupings. (Flegal, 2000b)
c. The prevalence of non-obesity overweight for U.S. adults 20-74 years of age did not change very much over the period 1960-1994, but the prevalence of obesity (BMI>30) changed dramatically in that same time period, from 12.8% to 22.5%. (Flegal, Carroll, et al., 1998; Kuczmarski, Flegal, et al., 1994)
d. Overweight in general and obesity in particular continued to increase up to the year 2000 in all age groups. (Flegal, Carroll, et al., 2002; Ogden, Flegal, et al., 2002; Ogden, Troiano, et al., 1997; Troiano, Flegal, et al., 1995)
e. The BMI frequency distributions were more negatively skewed (longer "tail" to the left, higher "hump" on the right) for NHANES III than for NHANES II. (Flegal & Troiano, 2000)
f. Differences between BMI-for-age and weight-for-stature were greatest for the shorter children aged 2-5 years in the NHANES III sample (n = 4348). (Flegal, Wei, & Ogden, 2002)
g. Data from the Second National Health and Nutrition Examination Survey (NHANES II) and from the NHANES I Epidemiologic Follow-up Survey indicated that 5.3% of females and 2.3% of males had an increase of five or more BMI units. [That's a big increase!] (Kuczmarski, 1992)
h. Mean BMI for the oldest Americans (>80 years of age) in NHANES III was considerably less than that of other age groups, suggesting the possibility of malnutrition in some of the oldest subjects. (Kuczmarski, Kuczmarski, et al., 2000)
i. Different cutting points for BMI yielded different percentages of overweight persons in NHANES III, but using the BMI >25.0 definition the overweight percentage is 59.4% for men and 50.7% for women. (Kuczmarski, Carroll, et al., 1997)
[I probably shouldn't say this, but I have the feeling that those folks "milked" too many publications out of their studies.]
There have been many other BMI investigations. The following are some of the findings (in alphabetical order, by first author):
Casey, Dwyer, et al. (1992): From the abstract: "...BMIs before maturity were poor predictors of middle-aged BMI status in females but were good predictors in males. The correlation between females' BMI in childhood and their BMIs at two points during middle age (40 and 50 y) was zero; in males it was r = 0.36 and 0.41, respectively... Linear-regression analysis was also used to assess the predictability of relative body size in middle age from earlier measures; BMI in childhood accounted for 0% of the variance in females and 17% in males. We conclude that the prediction of ponderosity in middle age from BMIs early in life is more reliable for males than for females."
Chai, Kaluhiokalani, et al. (2003): In their study of 1437 public school students in Hawaii the children of Hawaiian ancestry (HA) were similar to those who were not of Hawaiian ancestry in BMI, but both groups were well above the NHANES III averages. Twice as many HA and non-HA boys and girls were classified as obese.
Chang and Christakis (2003): They found that 27.5% of the women and 25.8% of the men in NHANES III mis-classified themselves with respect to self-perceived status as overweight, underweight, or about the right weight.
Davison and Birch (2001): In this longitudinal study of 197 girls (from age 5 to age 7) and their parents, an equation was derived for predicting change in BMI during that two-year period from BMI at age 5 and various other child and parent characteristics.
Dietz and Bellizi (1999): They defended the use of BMI as an indicator of overweight and obesity in children and adolescents, but they argued that the cutting point between overweight and obesity should be the same as that for adults.
Dwyer, Stone, et al. (2000): They studied 5106 children who participated in the Child and Adolescent Trial for Cardiovascular Health (CATCH) project. Their principal finding was that Hispanic children and African American children were getting heavier and fatter.
Freedman, Kahn, et al. (2003a): Using data from the Bogalusa Heart Study, they found that both childhood BMI and childhood height per se were good predictors of obesity in later life. In a letter to the editor of Pediatrics Karlberg and He (2003) questioned their findings, but in their reply Freedman, Kahn, et al. (2003b) defended them. Included in their defense was a reference to one of their earlier articles (Freedman, Kahn. et al., 2001).
Geraghty & Boone (2003): Reference has already been made to this study--with respect to the estimation of heights and weights. They also used abdominal computed tomography (CT) to derive an equation for predicting BMI from the CT measure. The correlation between actual BMI and estimated BMI was .893 for males and .919 for females.
Guo, Wu, et al. (2002): They developed a method for estimating the probability of adult overweight and obesity from childhood and adolescent BMI's. (See also the editorial by Bray, 2002 regarding their research.)
Helmchen & Henderson (2004): In this fascinating study the researchers used data from two sources, an ages 40-69 subsample (n = 12312) of a random sample (n = 35570) of men who had fought for the Union army in the Civil war (!) and a same-aged subsample (n = 4059) of non-Hispanic Whites from the NHANES I, II, and III surveys, and found that the average BMI increased by approximately 4.5 units on the BMI scale between the years 1890 and 2000. [That's also a big increase!]
Hlaing, Prineas, et al. (2001): Black children and White children in the Minneapolis Children's Blood Pressure Study (MCBPS) who were 6 to 9 years old at entry (n = 1302) were followed up for 12 years at 19 separate visits. Using starting level (SL) and asymptote (stabilized) level (AL) in BMI, they found a significant difference between White males and the other three groups (White females, Black males, and Black females) in SL; and between Black females and White females in AL.
Johnson (1997): This history of the evolution of the U.S. Army weight standards also includes a section on the use of BMI in conjunction with those standards.
Jolliffe (2003): Using the NHANES data and the definition of overweight as "at or above the 95th percentile of the revised Center for Disease Control (CDC) sex-specific BMI for age growth charts" [yes, that's quite a mouthful], Jolliffe found that the prevalence of overweight status for the age 2-19 group increased 182% between 1971 and 2000. They also found that the amount by which the BMI's exceeded the overweight threshold increased by 242%.
Launer and Harris (1996): They compared 19 different geographical groups of older persons with respect to height, weight, and BMI. Here are their results for the U.S. averages.
McGee (2003): As I indicated in Chapter 5, he studied the relationship between height and weight in various populations and found that weight did not always vary as the square of height (the supposed basis for the BMI formula). He also found that the relationship between height and weight is different for men and for women. He accordingly argued against single BMI standards for classifying men and women as underweight, normal weight, overweight, or obese.
McIntosh, Jordan, et al. (2004): They were concerned with the cut-off point on the BMI scale for anorexia nervosa. They found very little difference between two groups of subjects who had been diagnosed with anorexia nervosa--one group with BMIs below the "generally accepted" cut-off point of 17.5 and the other group with BMIs above 17.5.
Melnik, T.A., Rhoades, S.J., et al. (1998): In their study of a sample of 692 second grade and 704 fifth grade children in the New York City schools, they found overweight prevalences of 37.5% for the second graders and 31.7% for the fifth graders.
Mokdad, Serdula, et al. (1999): From the title of their article ("The spread of the obesity epidemic in the United States, 1991-1998") it is clear that they believe there is a serious problem in this country as far as overweight is concerned. They reported that the prevalence of obesity (BMI greater than or equal to 30) grew from 12.0% in 1991 to 17.9% in 1998.
Nolte, Franckowiak, et al. (2002): Just as they did for weight maximums, these authors provided the corresponding BMI maximums for the four principal branches of the U.S. military, and pointed out the disturbingly large percentages of young men and women who exceeded those maximums.
Oehlschlagel-Akiyoshi, Malewski, and Mahon, J. (1999): They studied various criteria for the diagnosis of anorexia nervosa, including the World Health Organizations's definition of a BMI below 17.5, and concluded that it would be better to use 85% of a subgroup's median BMI as the cut-off point rather than an across-the-board 17.5.
Overpeck, Hediger, et al. (2000). Using NHANES III data they found that changes in BMI before age 7 are predictive of overweight in adolescence and adulthood.
Plankey, Stevens, et al. (1997): They also used NHANES III data in determining the discrepancy between BMI based upon self-reported height and weight and BMI based upon actually measured height and weight. Linear regression equations were unable to compensate for the errors that would be involved in using self-reports. (See Chapter 16 for more on the matter of self-reported heights and weights.)
Popkin and Udry (1998): Using the data for a sample of 13783 adolescents in The National Longitudinal Study of Adolescent Health, they found the following obesity prevalences: White non-Hispanics 24.2%; Black non-Hispanics 30.9%; all Hispanic-Americans 30.4%; all Asian-Americans 20.6%. The prevalence of obesity was greater for males than for females in all ethnic subgroups except for Black non-Hispanics (male 27.4%, female 34.0%).
Rosner, Prineas, et al. (1998): They provided some very useful data regarding the frequency distribution of BMI for children and adolescents.
Schoenborn, Adams, and Barnes (2002): Based upon self-report data of height and weight for adults 18 years and older (n = 68556) in the National Health Interview Survey, they concluded that overweight (including obesity) was widespread (ouch--another bad pun!) in the United States, with 54.7% of the adult population having higher than desirable BMIs.
Seidell and Flegal (1997): In an article concerned with worldwide obesity, they reported that obesity as defined by BMI level varies considerably from country to country and even from region to region within country.
Stettler, Kumanyika, et al. (2003): They followed a cohort of 300 African Americans from birth to 20 years of age and found that rapid gain in early infancy was strongly associated with obesity in childhood and in young adulthood. (See also the editorial by Yanovski, 2003 regarding their research.)
Strauss and Pollack (2001): They studied 8270 children 4-12 years of age in the National Longitudinal Survey of Youth from 1986 to 1998, and found a rapid increase in overweight, especially among African Americans and Hispanics.
Stunkard, Berkowitz, et al. (1999): They were interested in the extent to which infants' weights are predictable from mothers' and fathers' weights for a sample of 38 women of normal weight and a sample of 40 obese women. They found very little difference between the average weight of the children of those two groups of mothers.
Sturm (2003): Using data from the Behavioral Risk Factor Surveillance System project, he estimated that between 1986 and 2000 self-reported BMIs of 40 or more (extremely obese) increased by a factor of four, from 1/2 percent of the adult population to 2 percent of the adult population.
Taubes (1998): He reported that there is not much evidence regarding the increase in overweight outside of the United States, and what little evidence there is is not very dependable.
Variyam (2002): In this general article the association between caloric intake and BMI was explored, with particular reference to its relevance for adult obesity.
Whitaker, Wright, et al. (1997): In their retrospective study of 854 subjects in a health maintenance organization in Washington state, they found that very early (under three years of age) childhood obesity was not a good predictor of adult obesity if the parents were not obese, but later (over 10 years of age) childhood obesity was predictive of adult obesity, regardless of parental obesity.
Williamson (1993): He reported a number of interesting findings regarding BMI based upon his analysis of the NHANES II data.
Wolf and Tanner (2002): In a general article concerned with both the prevalence and the treatment of obesity, they provided some evidence from NHANES that indicated an increase in average BMI (and therefore an increase in overweight) from 1991 to 1998. Their article also touched on BMR (see below).
The BMI’s of famous people
Of considerable interest, at least to many laymen and laywomen, are the heights, weights, and BMI’s of celebrities. Here are a few examples:
|Actor or Athlete |Height |Weight |BMI |
| | |in lbs. |Index* |
|Sylvester Stallone |5'9" |228 |34 |
|Arnold Schwarzenegger |6'2" |257 |33 |
|Sammy Sosa |6'0" |220 |30 |
|Harrison Ford |6'1" |218 |29 |
|George Clooney |5'11" |211 |29 |
|Bruce Willis |6'0" |211 |29 |
|Mike Piazza |6'3" |215 |27 |
|Brad Pitt |6'0" |203 |27 |
|Michael Jordan |6'6" |216 |25 |
Source: Today's Seniors web site.
There is a footnote to the table that reads:
"Obviously, these celebrities are neither obese nor overweight.
For the rest of us 'normal' people, a BMI Index value of 25-29.9
is considered to be overweight; a value of 30 or more
is considered to be obese."
Do you agree that they are all "neither obese nor overweight"? Does Arnold Schwarzenegger really weigh 257 pounds?!
What I find to be most interesting is the heights that are listed for entertainers and athletes vs. how tall they have been measured to be. The classic case is Alan Ladd, the popular movie star of the 40s and 50s, who was quite short (about 5ft 4in) but was said to be much taller. He even had to stand on a box when he was filmed in romantic scenes with women, e.g., Sophia Loren, who were taller than he was.
The books by Keyes (1980) and Samaras (1994) contain some fascinating anecdotes about other celebrities and what they tried to do to hide their shortness (and also some anecdotes about celebrities who were equally bothered by their tallness, particularly remarks such as "How's the weather up there?"). Dan Harbord's website lists the heights of well-known people (mostly entertainers) who are/were all 5'7" or less. You'll find several surprises (e.g., Napoleon Bonaparte--he wasn't as short as is commonly believed; Twiggy--she actually grew when she got older and was no longer an actress/model; Joseph Stalin; and Joan of Arc), unless you're really into knowing and caring about how tall various people are.
In any event, the evidence is clear. As a nation we've gotten fatter (greater average BMI's--see the Appendix to this chapter and the American Obesity Association's website for further information), but does that really matter? As I indicated above, the "effects" of overweight and obesity will be examined in Chapter 20. So I think that's enough about BMI for now, don't you? Let's turn to BSA.
BSA
BSA can be calculated by using one or more of five rather complicated formulas, which are given in:
1. Mosteller RD: Simplified Calculation of Body Surface Area. N Engl J Med 1987 Oct 22;317(17):1098 (letter)
2. DuBois D; DuBois EF: A formula to estimate the approximate surface area if height and weight be known. Arch Int Med 1916 17:863-71.
3. Haycock G.B., Schwartz G.J.,Wisotsky D.H. Geometric method for measuring body surface area: A height weight formula validated in infants, children and adults. The Journal of Pediatrics 1978 93:1:62-66
4. Gehan EA, George SL. Estimation of human body surface area from height and weight. Cancer Chemother Rep 1970 54:225-35.
5. Boyd E. The growth of the surface area of the human body. Minneapolis: University of Minnesota Press, 1935. (Obtained from: )
Source:
Bruen (1929) actually created a nomogram [a simple graphical device] for determining an individual’s basal metabolism, given his(her) height, weight, and BSA as calculated using the DuBois and DuBois formula.
BSA is often used by health care professionals to determine the appropriate dosages of drugs to prescribe for individuals (usually how many milligrams per square meter of body surface area). But some experts advise against using BSA as the basis for drug dosage, especially for anti-cancer agents (see, for example, Groshow, Baraldi, & Noe, 1990; Baker, Verweij, et al., 2002; Miller, 2002).
You can also get on the internet and calculate the appropriate drug dosage for a child, given the recommended dosage for an adult (see the pharmcal. website)
BIA
BIA is one method for determining body composition, e.g., percent body fat or the amount of fat-free mass in a given human body. (BMI makes no distinction between fat-free mass and fat-associated mass.) But there are other competing methods for determining body composition. (See Forbes, 1989 for an excellent general discussion of body composition.) Here are brief summaries of a few articles that are concerned with BIA and related matters:
The supplement to the September, 1996 issue of the American Journal of Clinical Nutrition was devoted entirely to BIA. Two of those articles are especially relevant to this book:
a. In a general article concerned with the standardization of BIA measurements, Kushner, Gudivaka, and Schoeller (1996) pointed out that certain individual and environmental characteristics (e.g., posture, food and beverage consumption, recent exercise) can affect BIA and need to be controlled.
b. Roubenoff (1996) used data from the Framingham Heart Study to compare BIA with both BMI and dual-energy X-ray absorptiometry (DXA) as estimators of percent body fat. He found BIA to be better than BMI and equally as good as DXA.
Others are:
Bandini, Vu, et al. (1997): They carried out a study of 132 pre-menarcheal, non-obese girls, and found that BIA was a good predictor of body fat, but was no better than triceps skinfold.
Burmaster and Murray (1998): Based upon the data for a sample of 646 veterans in Boston, Massachusetts, they derived a trivariate normal distribution that showed the relationships among body fat (as measured by BIA), height, and the natural logarithm (base e) of weight.
Chumlea, Guo, et al. (2002): They used height, weight, and BIA data for 15912 non-Hispanic Whites, non-Hispanic Blacks, and Mexican American participants in NHANES III ages 12-80 to derive sex-specific formulas for estimating total body water (TBW), fat-free mass (FFM), total body fat (TBF), and percent body fat (%BF). Males had higher mean TBW and FFM than females, whereas females had higher mean TBF and %BF for all ethnic groups; and mean TBF increased up until age 60 and decreased thereafter.
Fernandez, Heo, et al. (2003): For a sample of 487 male and 933 female Hispanic Americans, African Americans, and European Americans they found that the relationship between percent body fat and BMI for Hispanic American females is different from that for African American females and European American females. (The relationship between those two variables was similar for the three male ethnic groups.)
Fornetti, Pivarnik, et al. (1999): In their study of 132 female athletes at Michigan State University, they found both BIA and near-infrared interactance (NIR) to be very reliable and valid methods for estimating body composition.
Jackson, Pollock, et al. (1988): In a small study of 24 men and 44 women they found the BIA method of estimating body composition to be very reliable and as equally valid as a method involving BMI and other anthropometric variables.
Kuczmarski (1996): This was a commentary regarding the decision to include BIA measurements in NHANES III, which he agreed was a positive step, but he argued that the usefulness of such measures is limited by the lack of good equations for predicting body composition for various subpopulations.
Lohman, Caballero, et al. (2000): For a sample of 98 Native American children, they measured percent body fat using both BIA and various anthropometric measurements. They found that a combination of BIA, weight, and two skinfold measurements provided the best prediction of percent body fat.
Mott, Wang, et al. (1999): They were interested in the relationship between age and body fat. For a sample of 1324 volunteers (ages 20-94, both sexes, various ethnic groups) they developed curvilinear regression equations for predicting body fat (as measured by a combination of methods that did not include BIA) from age. Body fat was found to be lower for the elderly than for middle-aged persons.
Ruff (2000): Using existing data for Olympic-level athletes, Ruff derived formulas for predicting body mass from height and maximum pelvic breadth, and found those estimates of actual body mass to have an average prediction error of less than 3%.
Sun, Chumlea, et al. (2003), Owen (2003) and Sun, Wu, et al. (2003): In an issue of the American Journal of Clinical Nutrition in early 2003, Sun, Chumlea, et al. presented equations that they had derived for predicting total body water (TBW) and fat-free mass (FFM), as measured by BIA, from stature, resistance, and body weight. In a subsequent exchange of letters published later in the year in that same journal, Owen and Sun discussed the surprisingly low correlation between BMI and body fat and its relevance for the Sun, Chumlea, et al. research.
Zemel, Riley, and Stallings (1997): In an article that deals with nutritional assessment in general (the bibliography is excellent), they provide some interesting information about BIA as one of several methods for estimating various aspects of body composition such as amount of fat-free mass.
BMR
BMR has to do with the amount of basal energy expenditure (BEE) or resting energy expenditure (REE). It is usually estimated by using the Harris-Benedict (1919) equations:
For men, BMR = 66.5 + (13.75 x weight in kilograms) + (5.003 x height in centimeters) - (6.775 x age in years)
For women, BMR = 655.1 + (9.563 x weight in kilograms) + (1.850 x height in centimeters) - (4.676 x age in years)
These equations are appropriate for normal people with normal body fat, but not for the obese. (See Frankenfield, Muth, & Rowe, 1998.)
To estimate "actual" metabolic rate, BMR needs to be multiplied by an activity factor that is indicative of one's caloric needs. Consider the following example (taken from the crypticblue website):
| |
Example of Lisa's (a hypothetical woman) caloric needs:
The formula for women's BMR is:
BMR = 655.1 + (9.563 x weight in kilograms) + (1.850 x height in centimeters) - (4.676 x age in years)
Conversions:
To go from pounds to kilograms, divide pounds by 2.2046
To go from inches to centimeters, multiply inches by 2.54
Lisa's height, weight and age are:
Weight = 130 lbs, covert to kg: 130/2.2046 = 58.9676
Height = 5’ 5” or 65”, convert to cm: 65 x 2.54 = 165.1
Age = 41 years
Lisa's BMR = 655.1 + (9.563 x 58.9676) + (1.850 x 165.1) – (4.676 x 41) = 1332.726
Lisa's total caloric requirements are calculated as BMR of 1332.7 times activity factor, which is estimated as 1.7.
Lisa's Total Caloric Requirement = 1332.7 x 1.7 = 2265.59
So Lisa needs to eat 2266 calories each day to maintain her current weight.
BMR has been the focus of several articles. Here are brief summaries of some of them:
Liden, Wolowitz, et al. (2002): They compared the BodyMedia's SenseWearTM Armband with other more expensive devices for measuring energy expenditure and found it to be equally or more reliable and valid.
Seale and Conway (1999): Using indirect calorimetry (room-sized calorimeter) with a sample of 69 adult subjects (41 males, 28 females), they found that overnight energy expenditure (ON-EE) was very close to typical BMR.
Wolf and Tanner (2002): Included in their article were separate formulas for estimating BMR for women of ages 18-30, women of ages 31-60, men of ages 18-30, and men of ages 31-60. They also provided activity factors for bed rest (1.2), ambulatory (1.3), normal activity (1.5 to 1.75), and extremely active (2.0).
Zemel, Riley, and Stallings (1997): In this article that has already been referred to above (in connection with BIA), they provide a good summary of BMR (which they refer to as REE, but the two terms are synonymous).
One more B (body type)
Interest in various body types goes back hundreds of years. In his book, How long will I live?, Lawrence Galton (1976) refers to the two body types identified by Hippocrates c. 450 B.C. and the four body types in another system (unnamed) in 1700. But one of the first people to seriously classify body types was Sheldon (1940, 1942), who studied the bodies of approximately 4000 young men, divided them into three basic somatotypes that he called "endomorphs" (pear-shaped, i.e., hips wider than shoulders), "mesomorphs" (neither fat nor skinny), and "ectomorphs" (small-framed and thin). Recognizing that hardly anyone is a perfect ectomorph, mesomorph, or endomorph, Sheldon developed a three-variable seven-point-scale system of classification. A 7-1-1, for example, would be a perfect endomorph, whereas a 6-4-2 would be generally endomorphic but possess some muscular features and even a slight amount of ectomorphism. He also plotted each body type combination on a triangular diagram and attempted to associate each body type with certain personality characteristics. "Tracking The Elusive Human" website contains the following pictures of the basic (male) body types as well as other pictures and useful information regarding the Sheldon typology:
[pic] [pic] [pic]
Ectomorph Mesomorth Ectomorph
Things have gotten much more sophisticated since Sheldon first propounded those three basic body types and various combinations thereof. Stewart, Stewart, Williamson, et al. (2001), for example, have extended the concept of body type to body image (with an emphasis on female bodies--Sheldon studied only males) and developed a computerized measure of the latter through a technique called Body Morph Assessment (BMA--another three-letter "B" abbreviation!). And Carter (2003) has prepared a comprehensive instructional manual for determining various somatotypes according to Sheldon's three-variable, seven-point-scale system, along with rules for interpreting the various combinations for both men and women. [Interestingly, and amazingly, Carter never even mentions Sheldon's name!!] Formulas are provided for determining the various "amounts" of endomorphy, mesomorphy, and ectomorphy, and he gives pictures of two men, one of whom is a 1.6 - 5.4 - 3.2 and the other of whom is a 3.0 - 2.1 - 4.8. He also provides some evidence for the reliability and the validity of such measures.
Reference was made above to endomorphs as pear-shaped. The weight-loss literature contains a great deal of information regarding both pear-shaped and apple-shaped (most of the body fat around the waist) men and women. See the weight-loss- website for further information concerning "pears" and "apples" and how they are associated with Sheldon's somatotypes.
A fascinating article on body types in a different context is the discussion by Huh and Bolch (2003) of the relevance for radiation treatments of anatomic models based upon three-dimensional body surface equations, computed tomography (CT) and magnetic resonance (MR). Their article also includes some interesting data from the various NHANES surveys regarding changes in U.S. heights, weights, and BMI's.
CHAPTER 19: THE “EFFECT” OF HEIGHT
There have been numerous studies concerned with the "effect" OF height and weight on various variables or the "effect" of various variables ON height and weight. In this chapter and in the following chapter I would like to call your attention to the results of that first type of study.
[Let me again emphasize that the investigation of the relationship between height and something else is not like the investigation of the relationship between, say, drug dosage and pain, where drug dosage has been experimentally manipulated in such a way that subjects are randomly assigned to one dosage or another. Causality can be determined in the latter type of investigation. But we can't randomly assign people to be various heights and see what happens. Therefore the attribution of its “effects” will always be questionable.]
In the jargon of scientific research, when one is interested in assessing the “effect” of a variable X on another variable Y, X is called the "independent" variable and Y is called the "dependent" variable; i.e., the problem is to determine if, or the extent to which, Y "depends" on X. The dependent variable is always the more important variable, since it is "what counts"; the independent variable is merely potentially predictive of what counts.
I would like to concentrate on studies in which height (sometimes called “stature”) is the independent variable, since that is the more common situation, and summarize the extent to which height has been found to be predictive of physical variables such as blood pressure, morbidity, and mortality; and psychosocial variables such as income, self-concept, and quality of life.
[Warning: In some of the articles that are cited in what follows it is a bit difficult to determine which variable is taken to be independent and which is taken to be dependent; i.e., it is not clear in which direction the prediction of one from the other is intended.]
Breast cancer
There is a vast literature on the association between height and breast cancer. Are taller women more likely to get breast cancer than shorter women, or are shorter women more likely to get breast cancer than taller women? (Some men also get breast cancer, but the association of male height with the risk of breast cancer has not been studied, as far as I can tell.) Here are brief synopses of two studies that have been carried out on this topic. (See Chapter 20 for the results of studies that investigated the relationship between breast cancer and both height and weight.)
Palmer, Rao, et al. (2001): They investigated the relationship between height and risk of breast cancer for 64530 African American women aged 18-69 enrolled in the Black Women's Health Study. The principal finding was that the odds ratio was 1.6 for taller women (height greater than 69 in) as compared to shorter women (height less than or equal to 61 in); i.e., they were 60% more likely to develop breast cancer.
It would appear that there is a slight, but nevertheless noteworthy, tendency for taller women to have a greater risk of breast cancer than shorter women. (For accounts of some other investigations see Herrinton & Husson, 2001; Li, Malone, et al.,1997; and Palmer, Rosenberg, et al., 1995.) There is also an excellent summary of the relationship between height and the risk of breast cancer (and between weight and the risk of breast cancer--see next chapter) on the website for Cornell University's Program on Breast Cancer and Environmental Risk Factors (BCERF).
Other cancers
Most of the studies of the relationship between height and cancer have been concentrated on female breast cancer, there have been a few that were concerned with other cancers. Chen, Miller, et al. (2003) investigated the relationship between height and prostate cancer. The Chen group found that greater height is associated with slightly better survival.
Albanes, Jones, et al. (1988), Hebert, Ajani, et al. (1997) and Okasha, McCarron, et al. (2000) studied the relationship between height and cancer in general. Data from NHANES I were used by Albanes, Jones, et al., who found that shorter persons had a lesser cancer risk. Similarly, Hebert, Ajani, et al. reported that in their study of physicians the taller ones had the higher cancer rates. The findings of Okasha, McCarron, et al. have been the subject of a great deal of interpretation and misinterpretation, and they will be treated below under Mortality.
Heart diseases
The relationship between height and coronary risk has been the subject of a number of studies (e.g., Goldbourt & Tanne, 2002; Liao, McGee, et al., 1996; McCarron, Okasha, et al., 2000a and 2000b; Miura, Nakagawa, & Greenland, 2002; Mukamal, Maclure, et al., 2001; and Parker, Lapane, et al., 1998).
Goldbourt & Tanne (2002): In their study of 10000 adult Israeli males, they found little or no relationship between height and the risk of coronary heart disease (CHD).
Liao, McGee, et al. (1996): Using NHANES I data, they also found that the relationship between height and heart disease vanished when age and years of education were statistically controlled.
McCarron, Okasha, et al. (2002a): In their study of 8361 former students at Glasgow University, Scotland, they found a moderate but statistically significant relationship between height and cardiovascular disease, with the shorter men having the greater risk. Miura, Nakagawa, et al. (2002) questioned their interpretation of that finding and suggested that more attention be given to other and more important risk factors such as passive smoking and childhood infections. McCarron, Okasha, et al. (2002b) agreed with their critics regarding other risk factors, but defended their results concerned with height.
Mukamal, Maclure, et al. (2001): They reported an association between short stature and higher risk of acute myocardial infarction (MI) but found no association between short stature and earlier mortality. (See the discussion below regarding the relationship between height and mortality.)
Parker, LaPane, et al. (1998): This was another study that found a moderate but statistically significant inverse relationship between height and the risk of CHD, with shorter males having greater risk. More specifically, males who were taller than 5ft 9 3/4in had an 83% lesser risk than males who were less than or equal to 5ft 5in. (They found no such association for females.)
Stroke
One of the articles just cited (Goldbourt & Tanner, 2002) found that although the shorter subjects in their study had no greater risk of coronary heart disease they did have a higher risk of stroke than taller males.
Ventilatory problems
How height relates to forced expiratory volume and related matters was the focus of work by Allen (1989) who found that arm span as a surrogate for measured height is a good predictor of forced expiratory volume for elderly women who have lost height through osteoporosis and/or are physically unable to have their height measured in the traditional way (by a vertical stadiometer).
Diabetes
DiLiberti, Carver, et al. (2002) compared the heights of a sample of 451 diabetic children in a pediatric clinic with the heights of the same-aged children in NHANES III and found that taller heights were associated with greater risk of developing Type I diabetes.
Mental illness
In a study in which the roles of the variables as independent or dependent are not clear, Wyatt, Henter, et al. (2003) found little difference in height between military personnel who were diagnosed with psychiatric illness and those who were not. But even if an association had been found, would it have been alleged that differences in height "caused" differences in mental illness, or that differences in mental illness "caused" differences in height? [Apparently the former, since they refer to the hypothesis that "psychiatrically ill individuals were shorter"---which was not supported by their data.]
Birthweight
Pickett, Abrams, and Selvin (2000) studied a multi-ethnic sample of 8870 mothers and their offspring in San Francisco and found that when other confounding factors were controlled there remained a positive and statistically significant relationship between maternal height and infant birthweight for all subgroups except for Hispanic women. (See the reference to Schisterman, Moysich, et al., 2003 in the following chapter for a similar study of the relationship between maternal weight and infant birthweight.)
Mortality
Do taller people live longer than shorter people? Do shorter people live longer than taller people? Or is there no relationship between height and mortality? This has been a hotly-debated topic. Some of the arguments and some of the findings may surprise you.
The controversy revolves around the claim that short height is associated with short life. Some of the claimants of that hypothesis are Chen, Miller. et al. (2003) and Davey-Smith (2002). Some of those who are on the opposite side are Liao, McGee, et al. (1996) and Samaras and his colleagues (Samaras, 1978, 1994; Samaras & Elrick, 2002; Samaras, Elrick, & Storms, 2003a, 2003b--see above; Samaras & Storms, 1992), who claim that there is either no relationship between height and longevity or that shorter persons have an advantage. But what is the weight of the evidence (another bad pun)?
In their article in the Western Journal of Medicine, Samaras and Elrick (2002) review several studies that they claim support the hypothesis of longer life for shorter people. [Included in their review were the investigations carried out by Hebert, Ajani, et al. (1997); Liao, McGee, et al. (1996); and Okasha, McCarron, et al. (2000), all of which were cited above.]
Davey-Smith (2002) directly addressed the claim of lesser life expectancy for taller people by Samaras and Elrick (2002). He argued that they were deceptively selective in their review and that the preponderance of the research literature indicated just the opposite--taller people have greater life expectancy. He cited in particular the work of Okasha, McCarron, et al. (2000) which Samaras and Elrick said supported their claim, but which he (Davey-Smith) insisted did not.
Psychosocial variables
Some of the most interesting, and unusual, studies are those in which the relationship between height and intelligence, height and self-esteem, height and success, etc. were investigated. Here are the findings of some of them, along with some sources that refer to one or more of those studies:
Braus (1993) pointed out that short men rarely make "best dressed" lists and
are generally discriminated against. She cited a study in which the authors
reported that shorter people have more school problems, have more
difficulties in finding a mate, and get lower salaries than taller people.
In his book, How long will I live?, Lawrence Galton (1976) [no relation to Francis Galton, I don't think] cited a comment by sociologist Saul Feldman that "any American male under 5 feet 8 inches is a victim of discrimination".
Hensley and his colleagues (Hensley, 1993, 1994, 1998; Hensley & Cooper, 1987) were concerned about the "effect" that height is alleged to have on a variety of personality variables, such as self-esteem, physical attractiveness, and occupational success. In several studies of those variables they found, for example, that shorter males experienced greater handicaps in dating relationships and lesser occupational success. They cited a study by Frieze, Olson, and Good (1990) in which the claim was made that for every increase of one inch in height there was an associated increase of $600 in annual salary (in 1990 dollars).
In a recent book (Size matters) that is concerned primarily with his own personal experience, but has lots of other useful information, Stephen Hall (2006) discusses several ways in which short men are at a disadvantage in our society. If you read nothing else about the “effect” of height on various psychosocial variables, read this one. Like Pool (1994, 2001), Hall writes extremely well.
Humphreys, Davey, and Park (1985) carried out an extensive longitudinal investigation (as part of the Harvard Growth Study of boys and girls aged 8-17) of the relationship between height and intelligence. The principal finding was that for girls the correlation between height at the early ages and intelligence at the later ages was surprisingly [to me, anyhow] high (about +.40); i.e., the taller girls had higher intelligence scores on the average.
Judge and Cable (2004) carried out what they claim to be “the most comprehensive analysis of the relationship of height to workplace success to date” (see their abstract), and I agree. Their work fully supports Braus, Galton, Hensley, Frieze, and Hall (see above) that tall height “pays off” (my term, not theirs).
Mangano (2002) bemoaned the fact that it is still OK to discriminate against short people; he called such heightism "the last bastion of discrimination".
In their book, Stature and stigma, Martel and Biller (1987) suggested that things are so bad that there is really only one socially ideal height for men: 6ft 2in!
Persico, Postlewaite, and Silverman (2004) claimed that the “effect” of height is all in the adolescent years. They actually recommend that methods for increasing the heights of short teens (see below) be seriously considered. [Make all of the boys 6ft 2in and get them to stay at that height?!]
Sandberg and Voss (2002): In their review of the literature on the psychological consequences of short stature they found that height in and of itself is not a very good predictor of quality of life, and they warned against the overuse of growth hormones with children who are short for their age.
I have only recently become aware of a vast literature on attempts to decrease height (see, for example, Drop, de Waal, & de Muinck Keizer-Schrama, 1998) and an equally vast literature on attempts to increase height. The former literature is concerned primarily with the use of steroids to try to reduce the heights of unusually tall female teenagers (for both medical and social reasons); the effect has generally been minimal. The latter literature is almost exclusively concerned with social reasons for wanting to be taller (mostly by adult males); see the website. [And I always thought that the only way to artificially increase one’s ultimate height is to use a procrustean bed!] Such an attempts could (but probably never will) be studied experimentally, with half of the interested parties randomly assigned to the shortening (lengthening) treatment and the remaining half used as controls. Causality could then actually be determined.
CHAPTER 20: THE “EFFECT” OF WEIGHT
I would like to change the order of the dependent variables in this chapter.
Mortality
One of the most often studied epidemiological topics is the relationship between weight and mortality, or, more specifically, the relationship between various measures of obesity and mortality. As I mentioned in Chapter 18, many health professionals claim that there is an "obesity epidemic"; that obesity is the second leading cause of death in the United States (cigarette smoking being the first); and that it is imperative that people who are overweight must lose those extra pounds. Here are summaries of some of the hundreds of studies that have been carried out on the topic:
Allison, Faith, et al. (1999): In their meta-analysis of several prospective cohort studies, they found that the relationship between BMI and mortality was essentially the same whether or not early deaths were eliminated from the analyses.
Allison, Fontaine, et al, (1999b): The first part of the October 27, 1999 issue of the Journal of the American Medical Association was devoted entirely to obesity. In one of those articles Allison, Fontaine, et al. estimated the number of deaths per year that could be attributed to obesity as approximately 280,000. They based that figure upon a compilation of the results of six large studies for which there were both obesity data and mortality data.
Calle, Thun, et al. (1999): For a cohort of more than a million adults in the Cancer Prevention Study II they found a consistent direct relationship between BMI and all-cause mortality, with the association stronger for Whites than for Blacks.
Diehr, Bild, et al. (1998): They studied 4317 men and women aged 65-100 who were non-smokers and found that there was an inverse relationship between BMI and mortality; i.e., death rates were higher for those of lower BMI. This was one of the few studies that did not support the hypothesis that there is a strong association between overweight and lesser longevity.
Dorn, Schisterman, et al. (1997): For a random sample of men and women in Buffalo, NY they found that the relationship between BMI and mortality was complex, with a strong association between overweight and increased mortality from heart diseases for women and for younger men, but not for older men.
Durazo-Arvisu, Cooper, et al. (1997); Durazo-Arvisu, McGee, et al. (1997); and Durazo-Arvisu, McGee, et al. (1998): In this series of three articles Durazo and his colleagues determined that there was not a clear-cut relationship between BMI and mortality. Using data from a variety of sources they found that the lowest death rates were not associated with the lowest BMI's, as some previous investigators had reported; nor was there a curvilinear relationship, with the greatest mortality for high and for low BMI's, as other studies had shown.
Fontaine, Redden, et al. (2003): They used the data from a variety of studies to estimate the maximum number of years of life lost (YLL) attributable to severe obesity as approximately 13 for White men and 8 for White women aged 20-30. The "effect" of severe obesity on YLL for Black men and Black women in that same age range was found to be negligible. The results of their study, which appeared in the Journal of the American Medical Association, provoked several letters that were subsequently published in the same journal (see the Fontaine, Redden, et al. reference at the end of this book for the various citations).
Garrison, Feinleib, et al. (1983): They argued that you must control for cigarette smoking when you study the relationship between weight and mortality. Using the data available at the time from the Framingham Heart Study, they found that lean men who were smokers had higher mortality rates than all but the most obese non-smokers.
Gordon and Doyle (1988): In their longitudinal study of 1910 men in Albany, NY they found that the lowest mortality was associated with the middle range of desirable weights, with the highest mortality rates associated with the extremes.
Lee, Manson, et al. (1993): In a longitudinal study of Harvard University alumni (n = 19297) who were followed up from the early 1960s to the late 1980s they found a small but statistically significant positive relationship between weight and mortality; i.e., those with greater BMI's generally had higher mortality risks.
Manson, Stampfer, et al. (1987): They investigated the combined results of 25 studies of the relationship between weight and mortality and concluded that after taking confounding variables into account minimum mortality (maximum longevity) was associated with the very lowest levels of BMI (those that are at least 10% below the national average).
Manson, Willett, et al. (1995): On the basis of their analysis of data for 115195 women in the Nurses' Health Study they concluded that the relationship between BMI and mortality was J-shaped; i.e., low BMI was associated with somewhat greater mortality and high BMI was associated with even greater mortality, when compared to the desirable BMI range.
McGinnis and Foege (1993, 1998): Their studies, which Mokdad, Marks, et al. (2004, 2005--see following entry) have replicated, cited poor diet and inactivity as the second leading “actual” cause of death (tobacco being said to be the leading “cause”). Those studies have often been (mis?)interpreted to indicate that obesity itself is the second leading “actual cause” of death.
Mokdad, Marks, et al. (2004): They found that poor diet and inactivity (again often wrongly equated to obesity) was getting close to overtaking tobacco as the leading “actual cause” of death (400,000 for diet/activity; 435,000 for tobacco). Based upon criticisms by Flegal, Groubard, and Williamson (2004) and Flegal, Williamson, et al. (2004), and others, they later issued a correction (Mokdad, Marks, et al., 2005) in which the estimate of 400,000 was revised downward to 365,000.
Peeters, Barendregt, et al. (2003): Using data for 3457 of the participants in the Framingham Health Study who were 30-49 years old at entry to construct a life expectancy table, they reported that overweight and obesity were associated with large decreases in life expectancy (ranging from 3.1 years for male overweight non-smokers to 13.7 years for male obese smokers).
Rogers, Hummer, and Krueger (2003): In their study of the relationship between BMI and mortality, they found that obese persons were much more likely to die than persons of normal weight. The difference was particularly striking for diabetes-related mortality.
Sorlie, Gordon, and Kamel (1980): They reported that in the FraminghamHeart Study the risk of mortality was greater for both lean and obese persons. That was contrary to the findings of the Build and Blood Pressure studies' claims that there was an ever-increasing mortality risk from low relative weights to high relative weights.
Wei, Kampert, et al. (1999): With a slight twist in emphasis they studied the relationship between cardiorespiratory fitness and mortality in three groups of men: normal weight, overweight, and obese (total n = 25714). In all three groups those with low fitness had a higher risk of both cardiovascular disease and all-cause mortality.
Willett, Browne, et al. (1985): In one of the earlier studies of the relationship between weight and the risk of breast cancer, Willett and his colleagues used data for pre-menopausal women in the Nurses' Health Study and reported that for those women the risk of breast cancer decreased with increased body size.
The following synopses are concerned with the "effects" of weight on the risk of a number of different diseases, whether or not those diseases subsequently lead to mortality.
Breast cancer
There are more sources for studies of the relationship between weight and the risk of breast cancer than there are for studies of the relationship between height and the risk of breast cancer. Here are a few of the findings for the weight/breast cancer relationship:
Cleary and Maihle (1997): They reviewed several studies of the relationship between BMI and the risk of breast cancer for pre-menopausal women vs. post-menopausal women, and pointed out that the findings of such studies are often contradictory.
Colditz and Rosner (2000): Using data from the Nurses' Health Study they identified weight as one of the risk factors (to age 70) for breast cancer.
Dignam, Wieand, et al. (2003): The focus of their research was on the recurrence of breast cancer. Women who were obese had no greater risk of recurrence than women who were not.
Huang, Hankinson, et al. (1997): They studied both weight and weight gain as predictors of the risk of breast cancer. Using data from the Nurses' Health Study (n = 95256) they found that higher BMI's were associated with lower breast cancer risks both before and after menopause. Weight gain was associated with higher risk after menopause, but had little or no association before menopause. (See also the editorial by Kelsey & Baron, 1997 regarding this study.)
Love (2000): In Parts 4-7 of her book, Dr. Love discusses breast cancer in great detail. In that section (on page 292) she includes a table taken from a paper by Miller (1987) in which the attributable risk for breast cancer is said to be 12% (compared to attributable risks of 26%, 17%, and 8% for high-fat diet, age 25 or greater at time of first birth, and estrogen replacement therapy, respectively).
McTiernan (2000): In this review of a number of epidemiological studies regarding the relationship between the risk of breast cancer and both BMI and energy balance, McTiernan concluded that sedentary lifestyle and obesity are indeed risk factors for breast cancer but both are modifiable.
Swanson, Brinton, et al. (1989): In this second of two studies regarding the use of anthropometry to predict breast cancer, Swanson and his colleagues reported an inverse relationship between weight-for-height and breast cancer risk for women under 50 years of age, but little or no relationship for women older than 50.
Other cancers
Lee, Sesso, et al. (2003): They found little or no "effect" of either BMI or amount of physical activity on the risk of pancreatic cancer in their study of alumni of Harvard University and the University of Pennsylvania (total n = 32687).
Cardiovascular and related diseases
Arnett, McGovern, et al. (2003): In a series of four longitudinal studies in Minnesota concerned with cardiovascular risk factors they found an encouraging trend in reduced smoking and hypertension, but a corresponding trend in increased BMI.
Brown, Higgins, et al. (2000): Using the NHANES III data, they found a strong association between high BMI and high blood pressure. (See also the editorial by Flegal, 2000a regarding this research and the research by Must, Spadano, et al., 1999 cited below.)
Kelder, Osganian, et al. (2002): They were concerned with the change in the risk of cardiovascular disease. In their study of children who participated in the Child and Adolescent Trial for Cardiovascular Health (CATCH) they found that the relationship between BMI and cardiovascular risk remained fairly constant in a six-year period from third grade through eighth grade.
Manson, Colditz, et al. (1990): The Nurses' Health Study also provided the data for this investigation of the relationship between weight and the risk of coronary heart disease. They found that middle-aged women who were even moderately overweight had a much higher risk than women of the same age whose BMI's were in the desirable range.
Must, Spadano, et al. (1999) addressed the extent to which overweight and obesity are related to some diseases and not to others. On the basis of their analysis of NHANES III data for 16884 adults aged 25+ who had BMI's greater than or equal to 25, they concluded that increased BMI was associated with increased risk of every disease they studied except for coronary heart disease in men. (Unlike Brown, Higgins, et al., 2000, they did not find a high correlation between BMI and blood pressure. Both studies used some of the same data, but they differed in type of analysis employed.)
Willett, Manson, et al. (1995): Data from the Nurses' Health Study indicated that there is a fairly high risk of coronary heart disease even for women whose BMI's were within the recommended range of 21 to 27.
Other diseases
Leibson, Williamson, et al. (2001): This is one of those articles in which the distinction between independent variable and dependent variable is not clear. The first sentence of the abstract is "Increasing obesity within the general population has been accompanied by rising rates of diabetes." But which is the potential “cause” of which? The researchers studied the medical records of 1290 persons who had been identified as diabetics, and they found that the percentage of persons with BMI's greater than 30 increased over the course of the progress of the diabetes. Since obesity is associated with mortality (see above) they were concerned that the increase in BMI could lead to early death for obese diabetic subjects.
Paeratakul, Lovejoy, et al. (2002) were interested in how the relationship between obesity and the prevalence of various diseases might vary for men vs. women, for persons of different races, and for different socio-economic levels. The principal finding, based upon data obtained in the Continuing Survey of Food Intake by Individuals (CSFII), was that increased body weight was associated with greater risks of diabetes, hypertension, and high serum cholesterol regardless of sex, race, or SES.
Arthritis was the focus of the research by Sahyoun, Hochberg, et al. (1999). Using data from the NHANES 1982-1984 follow-up study they determined that women who had a BMI greater than 32 had a significantly greater risk of developing arthritis than women in the more desirable ranges.
[See Manson, Skerrett, & Willett (2002) for more on the “effects” of obesity on various health outcomes.]
Blood pressure
Gerber and Stern (1999) reviewed the literature on the “effect” of body size and body mass on blood pressure and found that overweight persons had higher blood pressures, but the amount of the discrepancy was largely due to differences in sexual maturity.
Birthweight
In an example of weight on both sides of the equation, Schisterman, Moysich, et al. (2003) applied Bayesian statistical methodology to data taken from the New York State Angler Cohort Study [yes, the participants were "fisherpersons"] and found a high positive correlation between maternal weight gain and infant birthweight.
Age at menarche
The research by Anderson, Dallal, and Must (2003) had a dual purpose. They were interested in both the trend in age at menarche and the extent to which weight (and race) might have influenced that trend. Using NHANES I, II, and III data they found a drop of about 2.5 months over a 25-year period, with an accompanying increase in relative weight.
Costs
Economists are always interested in costs and benefits. Obesity apparently has many costs and few benefits. Colditz (1992), for example, estimated the economic costs attributable to obesity in 1986 to be approximately $39.3 billion. Allison, Zannolli, and Narayan (1999) concentrated on the percentage of direct health care costs, not the actual dollar costs, that were associated with obesity. They questioned the then-estimated figure of 5.7% and claimed that if the earlier mortality of obese subjects were taken into account the better estimate would be somewhere between .82% and 4.32%. Finkelstein, Fiebelkorn, and Wang (2004) provided state-by-state data regarding the estimated annual costs of obesity; they ranged from $15 million for Wyoming to $1.7 billion for California. And in a letter to the editor of the American Journal of Preventive Medicine, Dannenberg, Burton, and Jackson (2004) claimed that in the year 2000 the airlines spent approximately 275 million additional dollars on extra fuel needed to accommodate the recent increase in body weight of passengers!
Energy expenditure
Leibel, Rosenbaum, and Hirsch (1995): In a study of 18 obese and 23 non-obese subjects that was concerned with both BMI and BMR, they found that a decrease in BMR accompanied attempts to maintain lower BMI's by losing weight.
Psychosocial variables
The psychosocial variable that is most often studied in conjunction with weight is quality of life. In one such study (Hassan, Joshi, et al., 2003) of 182372 adults who participted in the Behavioral Risk Factor Surveillance System (see some of the previous chapters for more information concerning that project), the obese subjects reported significantly more "unhealthy days" than their non-overweight counterparts. And in their recent article, Yan, Daviglus, et al. (2004) provided the results of their mailed survey of 3981 males and 3099 females, in which they found that overweight and obese elderly subjects had a poorer quality of life than those of normal weight.
In a very brief article with the very same title as the book by Hall (2006) [see previous chapter], Gardyn (2003) [this one came first] reported the results of a survey of 9882 adult women conducted by Simmons Market Research Bureau, in which it was found that underweight women were much more likely to want to go shopping with their friends than overweight women (the latter generally preferred to shop alone), enjoyed it more, and spent less time browsing.
Weight (actually relative weight) was found by Geier, Foster, et al. (2007) to be predictive of school attendance. Overweight children were absent statistically significantly more often than children of normal weight. The difference was approximately two days per year, on the average.
Other studies
Okosun, Choi, et al. (2001); Okosun, Liao, et al. (2000); and Okosun, Tedders, et al. (2000): Okosun and his colleagues used NHANES III data to study a variety of relationships involving BMI. They found, among other things, that women with similar high BMI's have quite different waist circumferences (greater for Whites than for Blacks and Hispanics); that there is a negative relationship between birthweight and fatness of children 5-11 years of age; and that obesity is associated with low perceptions of one's own health.
In support of their position regarding humans, Samaras and Elrick (2002) cited a study by Li, Deeb, et al. (1996), which showed that there is an inverse relationship between size and longevity for dogs.]
CHAPTER 21: THE COMBINED “EFFECT” OF SHAW SUBSETS
About ten years ago my colleague and former student, Jean Brown, now dean of nursing at SUNY Buffalo, asked me if I would like to be a co-author of a paper that she and her former dissertation adviser, Karen Radke, were working on. They were interested in the extent to which sex, age, height, and weight are predictive of various outcome variables such as forced expiratory volume, cancer-related weight loss, and physiological concentrations of various sorts. I agreed to do so, and we published the results in Nursing Research (Brown, Knapp, & Radke, 1997). Utilizing four different data samples we found R-squares ranging from .06 (for cancer-related weight loss) to .56 (for forced expiratory volume).
That got me thinking about how those four “SHAW” variables really do tell you a lot about a person, as I pointed out in the Preface to this book. [There's a neat website (All About Moms) where you can predict a child's adult height from his/her sex, age, height, and weight, and mother's height and father's height. They cite Khamis & Roche (1995) as providing the basis for such estimates.]
In so doing they should also be predictive of a lot of interesting variables, not just adult height and the variables that Jean, Karen, and I had studied. In the rest of this last chapter of my book I would like to share with you what I’ve discovered.
There are 11 combinations of two or more of the four variables: sex and age; sex and height; sex and weight; age and height; age and weight; height and weight [those are the twosomes]; sex, age, and height; sex, age, and weight; sex,height, and weight; age, height, and weight [the threesomes]; and sex, age, height and weight [all four]. My review will be structured according to some of those combinations.
Sex and age
In her dissertation at the University of Central Florida, Kolasinski (1996) studied the effect of age, sex (she called it gender), mental rotation ability, and postural stability on sickness that is associated with the playing of "virtual" computer games. [Her dissertation can be downloaded in its entirety on the internet, which in itself is an unusual and desirable option.] The subjects (n = 40) ranged from 19 to 46 years of age. She found (among many other things) that age alone was not a statistically significant predictor of sickness, but its interaction with mental rotation ability and with postural stability was.
[There is a rather large body of literature indicating that age often plays this “moderator variable” role. A moderator variable (not to be confused with a mediator variable--see Baron & Kenny, 1986; Lindley & Walker, 1993) is a variable consisting of two or more categories for which the relationship between two other variables differs from category to category. It is fairly common to discover that the correlation between two variables is not the same at all ages, resulting in an age-by-something interaction. If you find some of such terms to be confusing you can look them up in the Powers & Knapp (2005) dictionary.]
Age and weight
Another example of age as a moderator variable is found in the research by Stevens, Cai, et al. (1998), who studied the mortality experience in a 12-year period from 1960 until 1972 of over 300,000 people (men and women) who had no serious health problems at baseline. The relationship between body mass index (BMI) and mortality varied from one age to another, with the greater risk for younger subjects, but the relative risks for higher BMI were only slightly greater than 1 for each of the age intervals, albeit statistically different from 1, due to the huge sample size. (To my personal dismay, the authors appear to over-emphasize the fact that the confidence intervals for the relative risks do not include 1, and they correspondingly over-emphasize the actual magnitudes.)
Colditz, Willett, et al. (1987) looked at the "effect" of age (not as a moderator variable), weight, and other variables on the reliability (reproducibility) of the responses to a dietary questionnaire. They found little difference in the reproducibility of responses for persons of various ages and weights.
Height and weight
In the two previous chapters I summarized some of the research on the “effect” of height and the “effect” of weight, taken separately. Here are some of the findings of studies of “effect” of height and weight, taken together:
Friedenreich (2001): In this review article he claimed the evidence suggests that as height increases the risk of breast cancer increases, and as weight increases the risk of breast cancer decreases.
Li, Stanford, and Daling, J. R. (2000): Based on their retrospective study of 479 women ages 50-64 with breast cancer and 435 "controls" they concluded it is the age at which women reach their maximum height that is important, with those reaching the maximum after age 18 having a smaller breast cancer risk than those reaching the maximum before age 13. [Strange, but interesting.]
London, Colditz, et al. (1989): Using data from the Nurses Health Study (n = 115534), they found that there was a weak relationship between height and the risk of breast cancer for postmenopausal women but virtually no relationship for premenopausal women. For premenomausal women, as weight increased the risk of breast cancer decreased.
Rodriguez, Calle, et al. (2002) reported in their study of 300537 postmenopausal women that the ovarian cancer mortality rates were lowest for the shortest women and highest for the tallest women. Those rates were also higher for overweight women than for women of normal weight.
Samaras, Elrick, and Storms (2003b) reviewed some of the literature on the relationship between cancer risk and a variety of variables including height, and concluded that heavier birthweight and longer birth length lead to greater adult height which in turn leads to greater risk of cancer and other health problems.
Shors, Solomon, et al. (2001): They investigated the relationship between height and the risk of melanoma, and between weight and the risk of melanoma. They determined that there was a greater melanoma risk for the tallest men (top quartile), but found no relationship between weight and such risk for either men or women.
Swanson, Jones, et al. (1988): Using some early NHANES data they found that taller women had a greater risk of breast cancer. They found no such greater risk for heavier women. (See also Swanson, Brinton, et al., 1989.)
van den Brandt, P., Speigelman, D., et al. (2000): In pooling the data from seven prospective cohort studies (including London, Colditz, et al., 1989--see above) they found a small but statistically significant positive relationship between height and the risk of breast cancer even after controlling for dietary and other risk factors, especially for postmenopausal women. The relationship between weight and the risk of breast cancer also varied for premenopausal vs. postmenopausal women.
Ziegler, Hoover, et al. (1996): They studied both height and weight (and within age) as risk factors for breast cancer for Asian-American women. The risk for taller women was found to be approximately double that of shorter women, as was the risk for heavier women in their 50s compared to lighter women in their 50s. They also found a number of complex relationships between weight and breast cancer risk. One of the principal findings was that reduced risk consistently accompanied recent weight loss.
Sex, age, and weight
There is a nice example on the Golden Helix/Helix Tree website, where blood pressure is the dependent variable and age, sex, body mass index, and whether a person smokes or not are the independent variables. In their analysis of the data, age (under vs. over 50) was the first "split", indicating that age does affect blood pressure. [The raw data are available as an Excel workbook.]
All four
There is an interesting real data set (from the Third National Health and Nutrition Examination Survey) that is downloadable, free of charge, from the internet. It consists of 80 observations on several variables. Here are the raw data (in Minitab output form) for five of them. Sex is coded 1 = male, 0 = female; age is in years; height is in inches; weight is in pounds; and cholesterol is in millograms.
ROW sex age height weight choles
1 0 17 64.3 114.8 264
2 0 32 66.4 149.3 181
3 0 25 62.3 107.8 267
4 0 55 62.3 160.1 384
5 0 27 59.6 127.1 98
6 0 29 63.6 123.1 62
7 0 25 59.8 111.7 126
8 0 12 63.3 156.3 89
9 0 41 67.9 218.8 531
10 0 32 61.4 110.2 130
11 0 31 66.7 188.3 175
12 0 19 64.8 105.4 44
13 0 19 63.1 136.1 8
14 0 23 66.7 182.4 112
15 0 40 66.8 238.4 462
16 0 23 64.7 108.8 62
17 0 27 65.1 119.0 98
18 0 45 61.9 161.9 447
19 0 41 64.3 174.1 125
20 0 56 63.4 181.2 318
21 0 22 60.7 124.3 325
22 0 57 63.4 255.9 600
23 0 24 62.6 106.7 237
24 0 37 60.6 149.9 173
25 0 59 63.5 163.1 309
26 0 40 58.6 94.3 94
27 0 45 60.2 159.7 280
28 0 52 67.6 162.8 254
29 0 31 63.4 130.0 123
30 0 32 64.1 179.9 596
31 0 23 62.7 147.8 301
32 0 23 61.3 112.9 223
33 0 47 58.2 195.6 293
34 0 36 63.2 124.2 146
35 0 34 60.5 135.0 149
36 0 37 65.0 141.4 149
37 0 18 61.8 123.9 920
38 0 29 68.0 135.5 271
39 0 48 67.0 130.4 207
40 0 16 57.0 100.7 2
41 1 58 70.8 169.1 522
42 1 22 66.2 144.2 127
43 1 32 71.7 179.3 740
44 1 31 68.7 175.8 49
45 1 28 67.6 152.6 230
46 1 46 69.2 166.8 316
47 1 41 66.5 135.0 590
48 1 56 67.2 201.5 466
49 1 20 68.3 175.2 121
50 1 54 65.6 139.0 578
51 1 17 63.0 156.3 78
52 1 73 68.3 186.6 265
53 1 52 73.1 191.1 250
54 1 25 67.6 151.3 265
55 1 29 68.0 209.4 273
56 1 17 71.0 237.1 272
57 1 41 61.3 176.7 972
58 1 52 76.2 220.6 75
59 1 32 66.3 166.1 138
60 1 20 69.7 137.4 139
61 1 20 65.4 164.2 638
62 1 29 70.0 162.4 613
63 1 18 62.9 151.8 762
64 1 26 68.5 144.1 303
65 1 33 68.3 204.6 690
66 1 55 69.4 193.8 31
67 1 53 69.2 172.9 189
68 1 28 68.0 161.9 957
69 1 28 71.9 174.8 339
70 1 37 66.1 169.8 416
71 1 40 72.4 213.3 120
72 1 33 73.0 198.0 702
73 1 26 68.0 173.3 1252
74 1 53 68.7 214.5 288
75 1 36 70.3 137.1 176
76 1 34 63.7 119.5 277
77 1 42 71.1 189.1 649
78 1 18 65.6 164.7 113
79 1 44 68.3 170.1 656
80 1 20 66.3 151.0 172
Here's the full-blown multiple regression analysis :
regr c5 4 c1-c4
The regression equation is
choles = 919 + 180 sex + 0.37 age - 15.7 height + 2.07 weight
Predictor Coef Stdev t-ratio
Constant 919.5 616.1 1.49
sex 179.86 72.95 2.47
age 0.371 2.289 0.16
height -15.72 10.45 -1.50
weight 2.068 1.004 2.06
s = 241.0 R-sq = 15.6% R-sq(adj) = 11.1%
Analysis of Variance
SOURCE DF SS MS
Regression 4 804330 201082
Error 75 4355818 58078
Total 79 5160148
SOURCE DF SEQ SS
sex 1 476478
age 1 45402
height 1 36174
weight 1 246275
Unusual Observations
Obs. sex choles Fit Stdev.Fit Residual St.Resid
22 0.00 600.0 473.3 108.4 126.7 0.59 X
37 0.00 920.0 211.0 50.0 709.0 3.01R
57 1.00 972.0 516.4 85.4 455.6 2.02R
68 1.00 957.0 375.7 41.2 581.3 2.45R
73 1.00 1252.0 398.5 44.1 853.5 3.60R
R denotes an obs. with a large st. resid.
X denotes an obs. whose X value gives it large influence.
The principal findings are these:
1. The prediction is not very good. The multiple R-square of 15.6%, i.e., .156, is not much larger than the r-square for sex alone, which is (.304)2 or .092. And that's for the unadjusted R-square. The adjusted (for the fact that there are "only" 80 observations for five variables) R-square of .111 is only a little bit bigger than the .092.
2. Sex is still the best predictor, even when statistically controlling for the other three predictors. It's the only variable that has a significant (at the .05 level, anyhow) regression coefficient, if statistical significance makes any sense. [It does, if the sample has been randomly drawn; it doesn't if not. The information on the internet regarding this sample suggests that it has not. It is just a subset of the larger NHANES sample.
3. Height is what's called a "suppressor variable", as indicated by its positive correlation with cholesterol (.198) and its negative regression coeficient (-15.7).
Bottom line: My favorite four variables comprise a lousy set of variables for trying to predict cholesterol level. Such is life.
REFERENCES
Notes:
1. I refuse to include all of the names of authors of books and articles for which there are four or more co-authors. [The van den Brandt, Speigelman, et al. (2000) article, for example, has 18 co-authors. That's crazy!] Using the names of the first two authors in conjunction with "et al." should work just fine for the retrieval of such sources.
2. As you can tell, this list of references comprises approximately 20% of the entire book, which is probably too much, but I thought it would be better to err by having too many references rather than having too few. And most of the references contain even more references, some of which may be of additional interest to you but are not included here.
3. The numbers in parentheses at the ends of the references are the numbers of the chapters in which the various references are cited.
Abraham, S., Johnson, C.L., & Najjar, M.F. (1979). Weight and height of adults 18-74 years of age. Washington, DC: U.S. Government Printing Office.
Adams, C. (1994). Return of the straight dope. New York: Ballantine Books. [Cecil Adams' website, cecil@, also known as "The Straight Dope" website, provides all sorts of interesting (and funny, although occasionally a bit ribald) information that Cecil has collected into several books, including this 1994 book. If you haven't visited it yet, please do.]
Ahmad, S. (2005). The cost-effectiveness of raising the legal smoking age in California. Medical Decision Making, 25, 330-340.
Akhtar-Danesh, N., & Dehghan-Kooshkghazi, M. (2003). How does correlation structure differ between real and fabricated data sets? BMC Medical Research Methodology, 3 (18), 1-9.
Albanes, D., Jones, R.Y., et al. (1988). Adult stature and risk of cancer. Cancer Research, 48, 1658-1662.
Allen, S.C. (1989). The relation between height, arm span, and forced expiratory volume in elderly women. Age and Ageing, 18,113-116.
Allison, D.B., Faith, M.S., et al. (1999). Meta-analysis of the effect of excluding early deaths on the estimated relationship between body mass index and mortality. Obesity Research, 7, 342-354.
Allison, D. B., Fontaine, K. R., et al. (1999). Annual deaths attributable to obesity in the United States. Journal of the American Medical Association, 282 (16), 1530-1538.
Allison, D. B., Zannolli, R., et al. (1999). The direct health care costs of obesity in the United States. American Journal of Public Health, 89 (8), 1194-1199.
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