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STATWAY? STUDENT HANDOUTLesson 1.1.2 Samples, Populations, and Types of Statistical Studies STUDENT NAMEDATEINTRODUCTIONIn Lesson 1.1.1, we studied the four step process used in many statistical investigations. Step 1 in that process was “Ask a question that can be answered by collecting data.” We ask questions about one or more characteristics of each subject. In this context, the subjects of a statistical investigation are the individuals involved in the study. The subjects are often people, but can be animals, plants, or things. For example, in the previous lesson, the students in the class were our subjects. We asked if our personality traits were related to zodiac sign. The characteristics we studied were sets of personality traits and birth date groups. The characteristics that we study about each subject are called variables. In the example, the variables were sets of personality traits and birth date groups. In a statistical study, we usually ask one of the following types of questions:Research Questions about Populations A population is a set or group of people or objects that share certain characteristics. Research questions about populations include:Estimating a numerical population characteristic.Testing a claim about a population. Comparing two or more populations. Asking whether two variables are related in the population of interest.Research Questions about how one variable responds as another variable is manipulated or changedResearch questions of this type include:“What is the effect of …?” “What happens when…?”Try These 1Here is one of the studies we examined in the previous lesson.Researchers at the Center for Reproductive Medicine at Brigham and Women’s Hospital wondered what proportion of women who visit a fertility clinic would want the opportunity to choose the sex of a future child. They also wondered if those that would like to choose the sex were more likely to want a boy or girl. The researchers mailed a survey containing 19 questions to women who had visited the Center. One question on the survey asked women whether they would like the option of choosing the sex of a future child. If the response to that question was yes, a follow-up question asked whether they would choose a boy or girl. Of the 229 women who wanted to choose, 89 (38.9%) said they would choose a boy and 140 (61.1%) said they would choose a girl. Based on their statistical analysis of these data, the researchers concluded that there is convincing evidence of an overall preference for girls among women wanting to choose the sex of a future child. The researchers based this conclusion on this fact: In a sample of 229 women, it would be very unusual to observe a percentage as high as 61.1%. This is unusual if there is really no preference for girls in the population of women who would like to select the sex of a future child.AWhat type of question does this study ask? Does it ask a question about a population or a question about how one variable responds as another variable is manipulated?BWhat is the population of interest in this study?CWhat variable is being studied for each subject in the study?2Here is the other study we examined in the previous lesson.Psychologists believe that people are less likely to do something if they think it will require a lot of effort. But, how do people decide what things they think will be hard and what things they think will be easy? Researchers at the University of Michigan wondered if written directions would affect how hard people thought a task would be. If the written instructions for how to do a task were difficult to read, would that affect how difficult people thought a task was? To investigate this, they performed an experiment. The researchers randomly divided twenty students into two groups of 10 students each. One group received instructions for an exercise routine printed in a font that was easy to read, and the other group received the same set of instructions printed in a font that was difficult to read. A sample of each font appears below. Each student read the instructions, and then they were asked how many minutes they thought the exercise routine would take. For the group that read the instructions printed in an easy-to-read font, the average number of minutes they thought the routine would take was 8.23 minutes. For the group that read the same instructions printed in the hard to read font, the average was 15.1 minutes. Based on the study data, the researchers concluded that the difference between these two averages was not likely to be due to chance. There was evidence that people think a task will be harder when the instructions are hard to read.This is the easy-to-read font that was used in the study.This is the hard-to-read font that was used in the study.AWhat type of question does this study ask? Does it ask a question about a population or a question about how one variable responds as another variable is manipulated?BWhat variable is being manipulated?CWhat variable responds to the variable being manipulated?Next StepsWhen we know what type of question a study asks and what the variable(s) are in the study, then we can move on to the second step of a statistical investigation. Step 2 in this four step process is “decide what to measure and then collect data.” We measure the variables. This is why it is important to understand what type of question we ask in a study and what the variables are.There are two types of studies used to collect data: observational studies and experiments. Observational StudyIn an observational study researchers study the variables of a population. One example is whether a mother who wants to choose the sex of her child would prefer a girl or a boy. Researchers usually observe a sample of the population. A sample is a subset or a selected number of people from one or more existing populations. For example, in the study above researchers only observe a certain number of all mothers who want to choose the sex of their children. Remember that an observational study is used to answer questions about characteristics of populations. Because the goal of an observational study is typically to learn about the population, it is important that the sample be representative of the population researchers are interested in. The individuals in the sample must be similar to the individuals in the whole population.ExperimentIn an experiment researchers observe how one variable (such as estimated length of time for a task) behaves under different conditions (such as the font of the instructions). The conditions are being actively manipulated by the researcher (e.g., giving some students the instructions in one font and other students the instructions in a different font). An experiment is used to answer questions about how one variable responds as another is manipulated. Because the goal of an experiment is to learn about the effect of the different experimental conditions, it is important to have similar groups for each of the different experimental conditions.In summary, there is no attempt to influence the results in an observational study. This is different from an experiment. In an experiment conditions are manipulated to see the response to each condition.Try These Now let’s look at 2 other studies and ask some more detailed questions about them.3Imagine that our college is having financial problems. The college announces that it will shorten library hours to save money. The library will be closed in the evenings and on the weekends. Some students think that it is okay to pay $20 more per semester to keep the library open in the evenings and on the weekends.We are interested in learning about the proportion of students at your college who would pay $20 more per semester to keep the library open in the evenings and on the weekends. We plan to select a sample of 100 students. We will ask each of these students whether he or she agrees with the fee increase.AWhat type of question does this study ask? Does it ask a question about a population or a question about how one variable responds as another variable is manipulated?BIs this an observational study or an experiment? If it is an observational study, what is the population of interest? What is the question we are asking about the population?If it is an experiment, what is the response? What is the variable that we think might affect the response? CSuppose that we collect data by asking 100 students who are entering the library whether they would pay the fee. Is this a good way to collect data? Why do you think this? DSuppose that we collect data by asking 100 students who are at the school gym if they would pay the fee. Is this a good way to collect data? Why do you think this? EThe goal is to obtain a sample of 100 students that is representative of students at the college. Give a better way to select 100 students than the two ways described in parts C and D. Why do you think your way is better? 4We are interested in learning whether jogging for longer amounts of time decreases the resting heart rate of college students. We want to see if there is a difference between:The resting heart rate of college students that jog 30 minutes three times a week for six weeks, andThe resting heart rate of college students that jog for only 15 minutes three times a week for six weeks. We plan to use 100 college students who do not currently jog and who have volunteered to participate as subjects in this study. Resting heart rate of each subject will be measured at the start of the study. Fifty of the students will participate in a jogging program where they get together three times a week and jog for 30 minutes. The other 50 students will get together three times a week, but will only jog for 15 minutes. At the end of six weeks, resting heart rate will be measured again. AWhat type of question does this study ask? Does it ask question about a population or a question about how one variable responds as another variable is manipulated?BIs this an observational study or an experiment? If it is an observational study, what is the population of interest? What is the question we are asking about the population?If it is an experiment, what is the response? What is the variable that we think might affect the response? CSuppose that we create the two groups for this study according to age. We group the 50 youngest volunteers in the 30 minute jogging group. We group the 50 oldest volunteers in the 15 minute jogging group. Is this a good idea? Why do you think this? DSuppose that we create the two groups for this study according to weight. We group the 50 volunteers that weigh the most into the 30 minute jogging group. We group the 50 volunteers that weigh the least into the 15 minute jogging group. Is this a good idea? Why do you think this? EThe goal is to divide the 100 volunteers into two groups so that there is a “fair” comparison between the 30 minute and 15 minute jogging groups. Give a better way to divide the 100 volunteers into two groups that is better than age in part (c) and weight in part (d). Why do you think your way is better? YOU Need to KnowIn summary, we ask two types of research questions. Each type of research question is answered by a different type of study. Observational studies are used to answer research questions about characteristics of populations. Experiments are used to answer research questions about how one variable responds as another variable is manipulated. IntroductionDrawing Conclusions from Statistical StudiesThe fourth step in the statistical process is drawing a conclusion. There are two types of conclusions that might be made from a study:Generalize from sample to population.Change in response is caused by experimental conditions (cause-and-effect conclusion).Both types of conclusions extend the data that are observed. This means that researchers try to say something beyond what was observed. In the conclusion, researchers try to explain what they learned in the study.One type of conclusion is called “Generalize from sample to population.” Remember that researchers usually only study a sample of a larger population. They try to pick a sample that is representative of the population they want to study. When researchers draw this type of conclusion, they are confident that what they observed in the sample is true for the larger population. The other type of conclusion is called “Change in response is caused by experimental conditions.” This means that the change in a sample’s response was caused by the manipulation in an experiment. The researchers manipulated a variable and if there was an “effect” or response this means the change was due to the manipulation. This means that we have noticed a significant difference in the response of one variable to the variable that is manipulated.The table below summarizes when each of these types of conclusions is reasonable.Type of ConclusionReasonable WhenGeneralize from sample to populationObservational study is conducted and the sample is representative of the populationChange in response is caused by experimental conditions (cause-and-effect conclusion)Experiment is conducted and groups assigned to experimental conditions are similarThe best way to choose a sample that is representative of the population is to use a random sample from the entire population. The best way to ensure similar groups for different experimental conditions is to use random assignment to the experimental groups. You will see more about these ideas in upcoming lessons, but without a random sample in an observational study or random assignment in an experiment, no conclusions can reliably be drawn.This implies the following:For observational studies, we should avoid making cause-and-effect conclusions, but it is possible to generalize from the sample to the population of interest if the study design incorporated random selection from the population.For experiments, it is possible to reach cause-and-effect conclusions if the study design uses random assignment to create the experimental groups. If an experiment uses both random assignment to create experimental groups and random selection from some population, it is possible to make cause-and-effect conclusions and to generalize these conclusions to the population.Think about the study of women who want to choose the sex of their child. Look at the design of the study. Is it reasonable to conclude that a majority of all women who want to choose the sex of their child would choose a girl? Explain why this is or is not a reasonable conclusion.Think about the study about font style and the amount of time the reader thinks the task will take. Is it reasonable to conclude that a font that is more difficult to read will cause a reader to think the task described in the instructions will take longer? Explain why this is or is not a reasonable conclusion.Try These1The SAT exam is used in admissions decisions by many four-year colleges and universities. Prior to 2005, the exam consisted of only multiple choice questions. In 2005 a writing section was added to the exam. Students taking the exam are given 25 minutes to write an essay on a particular topic. In 2006, The College Board carried out a study of 6,498 essays that were selected at random from the more than 1.4 million SAT exams taken in the 2005 – 2006 academic year. For this sample of essays, 15% were written in cursive and 85% were printed in block letters. The results showed that the average score for essays written in cursive was higher than the average score for essays that were printed.AIs this study an observational study or an experiment? Explain your answer.BIs it reasonable to conclude that writing the essay in cursive was the cause of the higher scores? Explain your answer? 2Many students like to listen to music while they study. A psychologist was interested in finding out whether music affects the ability to remember material that has been read. The psychologist randomly assigned volunteer students who said they liked to study while listening to music into two groups. Each group was told to read an essay about Pearl Harbor and the U.S. entry into World War II. One group read the essay in silence. The other group read the essay while music of a style of their choice played in the background. After reading the essay they took a brief test that asked the students to recall details about the essay. The psychologist concluded that students who listened to music while reading scored lower than students who read in silence.AIs this study an observational study or an experiment? Explain your answer.BWhat are two reasons for why the students who listened to music scored lower than the students who didn’t listen to music?CThe psychologist found that the difference was so large that it was unlikely due to chance variation alone. Is it reasonable to conclude that the music was the cause of the lower scores? Explain your answer.3An article published in the Archives of Pediatrics and Adolescent Medicine (“Display of Health Risk Behaviors on MySpace by Adolescents,” 2009) described a study in which researchers looked at a random sample of 500 publicly accessible MySpace web profiles posted by 18-year-olds. The content of each profile was analyzed. Researchers drew many conclusions. One of the conclusions was that MySpace profiles that listed a sport or hobby was associated with decreased references to “risky behavior.” Decreased references to “risky behaviors” means that there were fewer comments on the person’s profile with references to sex, drugs, or violence. AIs it reasonable to generalize the stated conclusion to all 18-year-olds with a publicly accessible MySpace web profile? What aspect of the study supports your answer? BNot all MySpace users have a publicly accessible profile. Is it reasonable to generalize the stated conclusion to all 18-year-old MySpace users? Why or why not? 4The April 20, 2009 issue of the magazine Sports Illustrated reported that the Oklahoma City Thunder, a professional basketball team, had a win-loss record for the 2008-2009 season that was actually worse for home games that were sold out (3 wins and 15 losses) than for home games that were not sold out (12 wins and 11 losses).ABased on these data, is it reasonable to conclude that a sell-out crowd is the cause of the team’s poor performance at sold-out home games? Can you think of another explanation for why the win-loss record might be worse for sold out games than for games that are not sold out? BDid random selection or random assignment play any role in the collection of these data? Take It Home“Sweet Potatoes Brighten Your Skin” is the headline of an article that appeared in the magazine Woman’s World (November 1, 2010). The article concludes that eating sweet potatoes causes skin to be healthier because it reverses age spots, blocks harmful UV rays in sunlight, and protects against skin dryness. Consider the following five hypothetical study designs. For each study, answer the following five questions:1Is the study described an observational study or an experiment? Explain your answer.2 Did the study use random selection from some population? 3 Did the study use random assignment to experimental groups?4 Is the conclusion “eating sweet potatoes leads to healthier skin” appropriate given the study description? Explain your answer.5 Is it reasonable to generalize conclusions from this study to some larger population? If so, what population?Study Design 1: Two hundred students were selected at random from those enrolled at a large college in California. Each student in the sample was asked whether he or she ate sweet potatoes more than once in a typical week. A skin specialist rated skin health for each student on a scale of 1 to 10. It was concluded that skin health was significantly better on average for the group that reported eating sweet potatoes more than once a week than it was for the group that did not.1Is the study described an observational study or an experiment? Explain your answer.2 Did the study use random selection from some population? 3 Did the study use random assignment to experimental groups?4 Is the conclusion “eating sweet potatoes leads to healthier skin” appropriate given the study description? Explain your answer.5 Is it reasonable to generalize conclusions from this study to some larger population? If so, what population?Study Design 2: One hundred people who live in Miami volunteered to participate in a statistical study. The volunteers were divided into two experimental groups based on gender, with women in group 1 and men in group 2. Those in group 1 were asked to eat 6 ounces of sweet potatoes daily for 3 months. Those in group 2 were asked not to eat any sweet potatoes for 1 month. At the end of the 3 months, a skin specialist rated skin health on a scale of 1 to 10 for each of the volunteers. It was concluded that skin health was significantly better on average for group 1 than for group 2.1Is the study described an observational study or an experiment? Explain your answer.2 Did the study use random selection from some population? 3 Did the study use random assignment to experimental groups?4 Is the conclusion “eating sweet potatoes leads to healthier skin” appropriate given the study description? Explain your answer.5 Is it reasonable to generalize conclusions from this study to some larger population? If so, what population?Study Design 3: Two hundred people volunteered to participate in a statistical study. Each person was asked how often he or she ate sweet potatoes and a skin specialist rated skin health on a scale of 1 to 10 for each of the volunteers. It was concluded that skin health was significantly better for those who ate sweet potatoes more than once a week than for those who did not eat sweet potatoes more than once a week.1Is the study described an observational study or an experiment? Explain your answer.2 Did the study use random selection from some population? 3 Did the study use random assignment to experimental groups?4 Is the conclusion “eating sweet potatoes leads to healthier skin” appropriate given the study description? Explain your answer.5 Is it reasonable to generalize conclusions from this study to some larger population? If so, what population?Study Design 4: One hundred people volunteered to participate in a statistical study. For each volunteer, a coin was tossed in order to place them into a group. If the coin landed head up, the volunteer was assigned to group 1. If the coin landed tail up, the volunteer was assigned to group 2. Those in group 1 were asked to eat 6 ounces of sweet potatoes daily for 3 months. Those in group 2 were asked not to eat any sweet potatoes for 1 month. At the end of the 3 months, a skin specialist rated skin health on a scale of 1 to 10 for each of the volunteers. It was concluded that skin health was significantly better on average for those in group 1 than for those in group 2.1Is the study described an observational study or an experiment? Explain your answer.2 Did the study use random selection from some population? 3 Did the study use random assignment to experimental groups?4 Is the conclusion “eating sweet potatoes leads to healthier skin” appropriate given the study description? Explain your answer.5 Is it reasonable to generalize conclusions from this study to some larger population? If so, what population?Study Design 5: One hundred students were selected at random from those enrolled at a large college. Each of the selected students was asked to participate in a study and all agreed to participate. For each student, a coin was tossed in order to place them into one of two groups. If the coin landed head up, the student was assigned to group 1. If the coin landed tail up, the student was assigned to group 2. Those in group 1 were asked to eat 6 ounces of sweet potatoes daily for 3 months. Those in group 2 were asked not to eat any sweet potatoes for 1 month. At the end of the 3 months, a skin specialist rated skin health on a scale of 1 to 10 for each of the volunteers. It was concluded that skin health was significantly better for those in group 1 than for those in group 2.1Is the study described an observational study or an experiment? Explain your answer.2 Did the study use random selection from some population? 3 Did the study use random assignment to experimental groups?4 Is the conclusion “eating sweet potatoes leads to healthier skin” appropriate given the study description? Explain your answer.5 Is it reasonable to generalize conclusions from this study to some larger population? If so, what population?+++++This lesson is part of STATWAY?, A Pathway Through College Statistics, which is a product of a Carnegie Networked Improvement Community that seeks to advance student success. Version 1.0, A Pathway Through Statistics, Statway? was created by the Charles A. Dana Center at the University of Texas at Austin under sponsorship of the Carnegie Foundation for the Advancement of Teaching. This version 1.5 and all subsequent versions, result from the continuous improvement efforts of the Carnegie Networked Improvement Community. The network brings together community college faculty and staff, designers, researchers and developers. It is an open-resource research and development community that seeks to harvest the wisdom of its diverse participants in systematic and disciplined inquiries to improve developmental mathematics instruction. For more information on the Statway Networked Improvement Community, please visit . For the most recent version of instructional materials, visit kernel.+++++STATWAY? and the Carnegie Foundation logo are trademarks of the Carnegie Foundation for the Advancement of Teaching. A Pathway Through College Statistics may be used as provided in the CC BY license, but neither the Statway trademark nor the Carnegie Foundation logo may be used without the prior written consent of the Carnegie Foundation. ................
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