Dr



Dr. Ji Handout 1

Soc 332

Methods of Social Research

CHAPTER 1 CONCEPTS AND THEORIES

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Social research method

Social research method describes the way that sociologists do scientific research. It covers a variety areas, primarily consisting of concepts and theories, steps in research process, measurement, censuses and samples, causation and causal models, research designs, survey research, field research, experimental research, content analysis, and writing report.

Difficulties in Social Science

Using scientific methods to study human beings can minimize the mistakes because common sense is not scientific and often leads to wrong conclusion.

Unlike natural science, behaviors of human beings are in constant change and very variable.

It is hard to have experiment on human beings.

Description and explanation

Social sciences are guided by two goals:

1) Description - to describe some aspects or characteristics of the world.

2) Explanation - to explain why things are the way they are.

Social scientists use concepts and theories to describe and explain parts of reality in society observed.

Concepts

A building block of science. They are abstract terms that identify a class of things to be alike (such as “animals,” referring to a huge class of numerous and various animals.)

Concept must be clear and apply to all possible members of that class.

1 Parsimony (Abstract)

The law of parsimony reads as follows:

Theories always attempt to explain the most with the least.

That is, to explain as much as possible with a theory that is as simple as possible. The more abstract the concepts, the better the concepts.

2 Utility

The search for good concepts cannot be guided by truth because definitions are neither true nor false. Scientific definitions are regarded as names that are simply assigned to something. Therefore, the ultimate test of concepts lies in their utility, namely, their usefulness in constructing efficient theories.

3 Clear boundaries

Efficient concepts must have clear boundaries that eliminate ambiguity about what a concept includes and does not.

School performance Marital quality

Religiosity Racial discrimination

Are these concepts are clear or intertwined or overlapped?

4 Naming is not explaining

Concepts are useful for classification but do not explain anything. Simply to name things does not tell us why, what, when, or how.

Powerless Normless

Isolation Deviance

Suicide

Are these concepts of naming or explanation to some social phenomena?

Theories

A theory refers to a particular kind of statement designed to explain something of general interest and application. These statements have two features: abstract and falsifiable.

1 Abstract

Theories are abstract statements that say why and how some sets of concepts are linked. Their purpose is to explain some portion of reality.

2 Falsifiable - it is possible to say what evidence would show them to be false.

That is, a real theory directs our attention to observations that would prove the theory to be false which implies empirical predictions and prohibitions.

Empirical research

Empirical research links theory to observations. It means to “observe through the senses.” Although theories cannot be touched that only exist in our mind, they can guide and tell us that certain observable things would or would not happen. These certain things can be touched and observed by empirical studies, which in turn, verifies theory.

Concepts and Indicators

Concepts

Concepts are the abstract terms that identify a class of “things” to be regarded as being alike. Concepts cannot be observed. Only the specific instances of concepts can be observed.

Social class, for example, is a concept that refers to a group of people who are alike in terms of prestige and wealth.

Occupation

Education

Income

Indicator

An indicator is an observable measure of a concept.

Income, for example, is an indicator to measure social class.

Number of prays a week, is an indicator of religiosity.

GAP is an indicator of school performance.

Theories and hypotheses

A theory

A theory is an abstract statement about reality.

A logical deductive-inductive system of concepts, definitions, and propositions, which states a relationship between two or more selected aspects of phenomena and from which testable hypothesis can be derived. Theories in sociology are intended to be descriptive, explanatory, and predictive of phenomena of interest to discipline and to its individual practitioners.

Sources of theories

1 from our imaginations and observations.

2 desire to explain something motivate theories

3 research results formulate theories and modify theories

The wheel of science

Dealing with the relationship between a theory and the empirical research.

There are two different modes of reasoning, deduction and induction. The former is commonly utilized for description while the latter is often used for exploration research.

1 Deduction logic (tui-lun)- from abstract to concrete

From theory to hypothesis

From hypothesis to observation

From general to specific

From known principle to an unknown but observable conclusion

Major premise: Conservatives oppose abortion.

Minor premise: Edward is a conservative.

Conclusion: Edward opposes abortion.

2 Induction logic (gui-na)- from concrete to abstract

From observation to empirical generalization

From empirical generalization to a theory

From the specific to the general

From a set of observations to a general conclusion

From a general conclusion to a principle

Observation: Bill, Mary, Tom, Robert, Peterson are from Wisconsin.

They all have Catholic as their religion.

Conclusion: People from Wisconsin are primarily Catholic.

Correlation

Correlation means “to vary in unison” or “to go together.” That is, when one variable changes, the other one will change accordingly, or vise versa.

Correlations can be positive or negative. A positive correlation exists when two variables

move in the same direction. A negative correlation exists when one variable moves in one direction while the other variable goes in the opposite direction.

Hypothesis

A hypothesis is an expected but unconfirmed relationship between two or more variables under study.

While a theory specifies a relationship among concepts, a hypothesis specifies a relationship to be observed among indicators.

Example

A theory Social class defines one’s attitudes and behavior – abstract and hard to

observe.

A hypothesis People with higher education are more likely to have higher income –

observable and testable.

The Null Hypothesis

A null hypothesis states that a relationship between two variables is unrelated. Null hypotheses are always stated in the form denying the prediction derived from the theory. Because whether to reject or to accept the predicted relationship, one will never be sure to prove the theory. The finding of a test may support the theory while the finding of another test may deny the theory. Hence we commit either Type I or Type II error.

In comparison, a research hypothesis states that a predicted relationship between two variables is related. A research hypothesis assumes the statement of a relationship that is in the direction derived from a theory.

Type I error - when a null hypothesis is rejected, one commits Type I error.

Type II error - when one fails to reject a null hypothesis, one commits Type II error.

Exploratory Research

Engagement in speculative research that make systematic observations of uncharted or little known phenomena in order to get an initial sense of what is going on.

Pure, Applied, and Evaluation Research

Pure research

The primary motive is directed by the desire to increase knowledge without regard for practical application. Such research usually involves theory testing, to refine or extend a theory.

Applied research

The primary purpose is to serve practical needs. Applied research may or may not involve theory testing (most does not).

Evaluation research

It is to assess the effectiveness of a program, policy, product, or procedure, and is usually commissioned by government agencies, business, or organizations such as schools, churches, or hospitals. This study may have an immediate practical payoff for a specific program but may add little or nothing to the stock of fundamental knowledge.

Dr. Ji Handout 2

Soc 332

Spring 2002

CHAPTER 2 STEPS IN THE SOCIAL SCIENTIFIC PROCESS

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Step 1 Selecting a Topic

What is a valid sociological topic?

On the macro level, one may want to know such broad matters such the military, race relations, and multinational corporations. On the micro level, one studies such individualistic matters as how people interact on street corners, how people decorate their homes at Christmas, or college students’ dating patterns, etc. Any topic in social environment will be a valid topic.

What do you want to know more about?

Following one’s curiosity

Following one’s drive of interests

Based on available funding

Consider the availability of data source

Topic

Maternal Influence and Children’s Marital Quality

Parental Educational Attainment and Children’s Performance at School

Parents Have Influence on Children

Religiosity and Law Abiding

Step 2 Formulating A Research Question / Defining the Problem

Specify exactly what you want to learn about the topic.

The goal is to develop research questions for empirical investigation

A research question needs to be transformed into a statement

- a preliminary to the formulation of a hypothesis

Example: (Do) Parents’ marital behaviors influence their adult children’s marital quality (?)

(Do) Parents’ socioeconomic status influence their children’s performance in school (?)

Research questions are not research hypotheses

Research questions include some concepts

Research hypotheses need to be operationalized indicators

Concepts need to be clearly defined prior to formulation of hypotheses

Appropriate indicators of the concepts must be selected and defined for hypotheses

Example: What are the parental marital behaviors?

What is adult children’s marital quality?

What is the parents’ socioeconomic status?

What do you mean about children’s school performance?

Step 3 Defining the Concepts

Many different concepts used by researchers

Some are generally understood while others are not

Socioeconomic status - education, income, occupation

Religious beliefs - Protestant, Catholic, Jewish, Others, None

Social class - based on income, or education, or prestige, or wealth, or power

Many competing definitions and one has to make the selections

Marital quality - marital happiness, relationships, togetherness, satisfaction,

Develop new concepts

Family violence - wife abuse, child abuse, elderly abuse, husband abuse?

Maltreatment, malnutrition, throwing objects, battering, spanking, hitting, killing, murders, rapes, etc.

Step 4 Operationalizing the Concepts

Operationalizing the Concepts by appropriate indicators

the process of developing effective and feasible indicators of the concepts

“Marital quality,” “religiosity,” “powerless,” “isolation,” “school performance,”

Marital quality

“Marital satisfaction between husbands and wives”

Social stratification

Slavery system, Caste system, Estate system, Class system

Class system-power, prestige, property

Property - income, wealth

Religiosity

Number of prays/day/week, frequency to church, regularity to church, perception of God as Mom, Dad, good deeds to people/ride/donation, etc.

School performance

GAP, attendance, rewards, presentations, papers published, leadership,

Use standard indicators

Concepts ( Indicators

Education attainment - years of school, degrees earned, 1+2?!)

Example: Party Preference*

1. Democrat

2. Republican

3. Independent

4. Other

5. No Preference

Religious Preference* Religious Preference

1. Protestant 1 Protestant

2. Catholic 2 Catholic

3. Jewish

4. Other

5. None

Place of Residence Place of Residence*

1. Urban 1 Urban

2. Suburban 2 Suburban

3. Rural 3 Rural, farm

4. Farm 4 Rural, nonfarm

Marital Status Marital Status*

1. Married 1 Married

2. Single 2 Single

3. Divorced 3 Divorced

4. Widowed 4 Widowed

5 Others

Exhaustive

The overall categories must be exhaustive, meaning that there must be sufficient categories so that all persons, objects, or events being classified will fit into one of these categories.

Mutual Exclusive

Categories must be mutually exclusive, meaning that the persons or things being classified must not fit into more than one category.

Ordinal

It is the process of ranking cases in terms of the degree to which they have any given characteristics. Numbers indicate the rank order of cases on some variable.

Cases are sorted into categories.

Categories can be rank ordered.

Example

An attitude toward abortion can be measured as the following ordinal variable:

1) Strongly disagree

2) Disagree

3) No opinion

4) Agree

5 Strongly agree

Marital satisfaction variable is measured at another ordinal variable:

1) Very unsatisfied

2) Unsatisfied

3) Average

4) Satisfied

5) Very satisfied

Higher scores represent more satisfaction with marital lives.

Interval

It is the process of assigning a score to cases so that the magnitude of differences between them is known and meaningful. Interval variable is measured using some fixed unit of measurement such as the dollar, the year, the pound, or the inch. Numerals represent mathematical equivalences on the variables being measured. Temperature: 0,10, 20, …90, 100, is another example.

A more precise form of ordinal

Categories can be rank ordered

Fixed unit of measurement

Interval between categories is of equal quantity

Example

Mothers’ educational attainment in years is indicated by a set of scales:

0) no education;

1) one grade;

2) two;

3) three;

4) four;

5) five;

6) six;

7) seven;

8) eight;

9) nine;

10) ten;

11) eleven;

12) twelve grades, completed high school;

13) one year of college;

14) two years of college;

15) three years of college;

16) four years of college;

17) 17+, 5 plus years of college.

Higher scores represent higher level of education.

Mothers’ income in dollars

It is indicated by the actual and the around number of dollars ranging from the lowest level to the highest level:

$800

$801

$802

…

…

$90,000

…

$99,997

Higher scores represent higher level of income.

Ratio

Like an interval variable, it has a standard unit of measurement.

Unlike an interval variable, a ratio variable has a non-arbitrary zero point.

The zero point represents the absence of the characteristic being measured.

Having equal intervals between categories

Having meaningful zero point

Ratio variables convey the most information and thus have the highest level of measurement.

The interval and ratio variables are often used interchangeably because there are not many truly interval variables in social sciences.

Example

World population birth rate = 2.2% (2001 world popu data sheet)

World death rate = .9%

World growth rate = 1.3%

World percent urban = 46%

United States birth rate = 1.5%

United States death rate = .9%

United States growth rate = .6%

United States = 75%

Levels of Measurement of Variables

__________________________________________________________________

Level Rank order to values? Fixed unit of measurement

__________________________________________________________________

Nominal No No

Ordinal Yes No

Interval Yes Yes

Ratio Yes Yes

Information Provided by the Four Levels of Measurement

________________________________________________________________________

Information

Provided Nominal Ordinal Interval Ratio

________________________________________________________________________

Classification X X X X

Rank Order - X X X

Equal Interval - - X X

Absolute Zero - - - X

________________________________________________________________________

Units of Analysis

The entities to which our theory and research applies

Things a hypothesis directs us to observe. They can be human beings or non-human beings; can be individuals or groups or aggregates.

Examples of units of analysis:

Individuals, students, married couples,

Basketball teams, court cases, stage plays,

Towns/cities, states or provinces, nations/countries, etc.

Aggregate Data

Individual scores or individual respondents are combined into larger groupings.

Data of this kind in which cases are larger units of analysis are called aggregate data.

Since we cannot question our cases such as a city, towns, schools, states, or nations, we create measures by summing or aggregating data on individuals within the larger unit. The population in Eau Claire, for example, is simply the sum of the individuals within its boundaries. Usually the raw numbers are turned into rates. Population density in Eau Claire, for example, is the ratio between population and land areas per square mile.

Examples for more aggregate data are birth rate, death rate, migration rate, murder rate, employment rate, dependency ratio, infant mortality rate, divorce rate, marriage rate, urbanization rate, etc.

Sources of medical care of the aged by gender and region in Hanan

_______________________________________________________

Male / Female

______________________________/_________________________

Urban Rural / Urban Rural Self 593 8273 / 3140 9658

9.0 92.7 / 42.5 96.5

Half-self 785 270 / 2299 318

11.9 3.0 / 31.1 3.2

Public 5200 384 / 1946 33

79.1 4.3 / 26.4 .3

Total 6578 8927 / 7385 10009 42.4 57.6 / 42.5 57.5 ________________________________________________________

Ecological Fallacy

Either inferring individual characteristics from analysis of aggregate data, or inferring aggregate characteristics from data for individuals, entails a logical error, called Ecological Fallacy.

Ecological Variables - If the larger units are spatial or geographic areas like states, provinces, or countries, the aggregate data are ecological data and their variables are ecological variables. Examples are murder rate, percent urban, average income, and percent Hispanic in the 50 states.

The quality of Measures

Reliability

A variable is reliable if it is consistent - if repeated observations give similar results. Reliability deals with consistency.

The extent to which the measurement of instrument procedures produces consistent and stable results on repeated trials.

Test-retest reliability

The same cases are measured at two different times, and correlation between the two scores is the estimate of the reliability of the measure

Alternate forms

Design two tests with same level of difficulties but administer each test to the same individuals at different times. The correlation between two scores reflect the reliability of the variable

Split halves

Indicators are divided by two equivalent half and both forms are administered in one test. The correlation between the scores on the two halves measures the reliability.

Internal consistency

a) Internal consistency seeks to determine if all of the items in a test are measuring the same thing. b) Each indicator is assumed to be a good measure of the same target concept. c) Cronbach’s alpha (α) is the mostly used approach. d) The value of alpha ranges from 0 - 1. “0” means not reliable; “1” means perfectly reliable; e) α = .7 is accepted as sufficiently reliable for use.

Example: Children’s Gender Role Belief (CGRB)

12013 Most of the important decisions in the life of the family should be made by the man of the house.

12014 When there children I the family, parents should stay together even if they don’t get along.

12015 It is perfectly all right for women to be very active in clubs, politics, and other outside activities before the children are grown up.

12016 There is some work that is men’s and some that is women’s and they should not be doing each other’s.

12017 A wife should not expect her husband to help around the house after he comes home from a hard days work.

12018 A working mother can establish as warm and secure a relationship with her children as a mother who does not work.

12019 It is much better for everyone if the man earns the main living and the woman takes care of the home and family.

12020 Women are much happier if they stay at home and take care of their children.

12021 It is more important for a wife to help her husband’s career than to have one herself.

12023 A man’s family should always come before his career. Would you say____

1) Strongly agree

2) Agree

3) Undecided

4) Disagree

5) Strongly disagree

α = .7357 (12013, 12019, 12020, 12021)

Inter-rater reliability/Inter-coder reliability

Using the same measuring instrument, two or more independent raters/coders place observations into the same category. If the measuring instrument is reliable, different observers should produce consistent results.

Example

“How do you code the following into two categories?”

Marital Quality (MQ):

Marital problems

Marital satisfaction

Marital disagreement

Marital happiness

Marital conflicts

Marital enjoyment

Marital abuse

Marital togetherness

Marital employment*

Marital division of labor*

Marital relations*

Marital finance*

Validity

The degree to which the empirical indicators measure what it purports to measure.

The extent to which the indicators measure what you intend to measure.

Face validity

The variable obviously measures the concept judging based on the face of it.

“How old are you?”

“ When were you born?”

Are questions obviously a valid measure for measuring the age of the respondent.

Convergent validity

Indicators of the same concept should be highly and positively correlated with one another. Indicators that represent the same concept should converge on a single, underlying, empirical base.

What are your test scores in math, physics, chemistry, biology, statistics, and computer science?

Are these scores are correlated to each other?

Are they valid measures to measure your GPA and/or IQ?

Criterion validity

Validity is established by determining how strongly the measure is correlated with a criterion variable that is external to the measurement instrument. It is to compare an indicator with a criterion one that is known as valid.

Education, Income, and Occupation are widely accepted criteria variables to measure one’s socioeconomic status (SES).

Can I use Education as a variable to measure class status?

Can I use Income as a variable to measure prestige?

Can I use Occupation as a variable to measure power?

Construct validity

This validity is rooted in its ability of the measure to work in theory. Validity of a measure is established by seeing if it meets the underlying assumptions. In other words, the validity of a measure is assessed through its relationship to other measures consistent with theoretical derived hypotheses.

Research Questions:

Do fathers impact their children’s temperament?

Do children’s occupation resemble their parents?

The validity of the measures is established by whether or not these measures are consistent with the theories: The Resource Theory, Socialization Theory, and The Theory of Intergenerational Effect.

Cross-case comparability

Valid measures must be comparable across cases. That is, questions must be understood the same way by all respondents. If the same question is understood differently and responded differently, meaningful comparisons are hard to make. (This is especially difficult when being used across nations).

“Please tell me in round numbers about the amount of income you received last year including your family incomes.”

$0, 1, 100, 1000, 10, 000, 20,000, … to $ 99,000.

Does the income include spouse’s income, children’s, other income like property, stocks, etc?

If understood differently, then how could one make comparisons meaningfully by gathering this kind of data?

A Variety of Measures

Survey questions and indexes

Survey questions

Surveys are the most common method for obtaining information in social science. Survey questions not only ask characteristics of the respondents but also questions about opinions and attitudes and self-reports of behavior such as drinking, shopping, reading, voting, attending church, etc. They meet the specific purpose of researchers.

Indexes

A number of similar questions that are designed to measure the same concept can be combined together known as an index. This index is based the assumption that more measures of the same thing will yield more sensitive measurements.

Scales

Scales and indexes are often used interchangeably.

Both provide a rank ordering of respondents along a continuum representing the traits of the target of measurement; both rely on multiple indicators of the traits to form composite measures. True scales weight the importance and intensity of the indicators used in the construction of the scales (Guttman).

An index and a 6-point scale to measure Religious Fundamentalism:

An index of Religious Fundamentalism:

a) Religion is a very important part of life

b) After I do something wrong, I fear God’s punishment

c) People who are evil in this world will suffer in Hell

d) Gods knows everything a person does wrong

e) In the end, God punishes those who have sinned

Each item was scored on a 6-point scale:

1= strongly agree

2= agree

3=somewhat agree

4=somewhat disagree

5=disagree

6=strongly disagree

Measures based on observations (Detailed in Chapter 10)

Measures based on actual recorded observation of the phenomenon of interests.

Observation provides both verbal and nonverbal behavior.

Observation can yield many measurements in other modes of research.

Rates and other aggregate measures

When units of analysis are aggregates such as towns, schools, states, or nations, we apply measures by summing or aggregating data on individuals within the larger units.

Rates

A rate is a proportion or ratio and is created by dividing one variable by another variable.

Rates create a common basis for comparison across aggregate units.

Rates are standardized measures because they express and compare differences between scores out of 100. They relate number of cases occurring to a 100.

Coding content to get measures

When units of analysis are not humans or aggregates of humans such as newspapers, movies, songs, or stories, they require a coder to make judgments about how cases should be categorized. To get measures, most researchers use content analysis.

Content analysis

A technique of transforming non-quantitative verbal, visual, or textual material into quantitative data to which standard statistical analysis technique can be applied.

UWEC Campus 001

Chippewa Valley 002

Wisconsin Daily 003

US Today 004

Washington Post 005

… …

200

Dr. Ji Handout 4

Soc 332

Spring 2002

CHAPTER 4 CENSUSES AND SAMPLES

______________________________________________________________________________

“ To learn basic concepts about census and samples

“ To explain how sampling works

“ To know the bases of random sampling

Census

“ The total process of collecting, compiling, and publishing demographic, economic, and social data pertaining, at a specified time or times, to all persons in a country or delimited territory (UN).

“ A census is an official count of the population and recording of certain information about each person in a country.

“ Data are collected from all cases or units in the relevant set.

Early censuses

“ Egypt, Babylonia, China, India, and Rome

“ Large-scale counts were registered as early as 5 B.C but not real-sense census.

“ Caesar Augustus, the Emperor of Rome, ordered that a census be taken of his empire. Everyone was required to return to his ancestral home (based on Bible).

“ To establish how many people and households there were within the territory under the ruler’s control and how much tax would be expected to pay.

“ To report the number of persons in every household and to list their significant possessions

Modern Census

Starting from late18th and early 19th century

Sweden is the first European nation to have census 1749

Denmark and several Italian states (before uniting of Italy) 1700s

The United States 1790

England 1801

Lebanon 1932

India 1881

China 1953

78% of world’s population was enumerated by censuses 1953-1964

81% of countries have or are planning to take census 1995-2004

Census of the United States

1. First census was conducted in 1790

2. A census is taken since 1790 for every 10 years (22 times)

3. The first 100 year-censuses were taken by US marshals

4. The Census Bureau took the job since 1902

5. The information asked is from simple to complex- from age, free or slave, name, aged 16 year older, white male or females, and other persons, to basic demographic and housing characteristics, to all other information such as sex, racial, ethnic, year of birth, marital status, nationality origin, literacy, death, suicide and murder, income, net worth, occupation, and place of birth, etc.

6. Who is included in the census?

Two ways:

de facto population – which counts people wherever they are found on the census day;

de jure population – which counts people where they legally belong to regardless whether they were there on the day of the census.

7 The United States adopts the method in between de facto and de jure, and includes people in the census on the basis of Usual Residence, which is roughly defined as the place where a person usually sleeps. College students may be counted at the college rather than counted at their parents’ houses.

Purpose of census

1. The government wants to know the accounts of taxpayers, laborers, and solders.

2. To study population process, change, and to make planning.

Population

“ Refers to all members of a nation.

“ It is not limited to human beings. In statistics, a population refers to all units constituting a set which is delimited (ding-jie-xian).

“ A population also refers to as the universe of units where the word of universe means “all things.” “All persons in India” defines a universe as does “all students in UWEC” or “ all women in WI.”

Samples

A subset of population

A selected section of a population

Random Selection

It is a process in which every case has an equal chance of being selected.

Random sample and probability sample are used interchangeably because they based on random sampling principle that all cases have a known probability of being selected.

Statistics and parameters

A statistics is a characteristic of a sample while a parameter is a characteristic of a population. A statistic is a value to describe a sample while a parameter is to describe the population. A statistic is the estimate of the parameter. An average income for Water ST, for example, is a statistic to describe residents in Eau Claire sample while the average income for all residents of America is a parameter.

Confidence interval and levels

We use a sample statistic to estimate a population parameter. Population mean may be greater or less than the sample mean. To estimate a population mean, we must establish a range around the sample mean within which we think the population mean lies. This range is called confidence interval.

It is a range around the sample mean within which population mean lies.

It is a range around the sample mean to predict the population mean.

It is a range within which we use a statistic to predict a parameter.

Two levels of confidence interval are commonly used: 95 and 99 percent.

95 percent confidence interval = 0 ± 1.96(0

The chances are 95 out of 100 that we are confident that population mean (() lies within this range-the confidence interval.

99 percent confidence interval = 0 ± 2.58(0

The chances are 99 out of 100 that we are confident that the population mean (() lies within this range-the confidence interval.

95 percent of the scores lie within 1.96 standard deviations of the mean. Thus we use this knowledge to find a confidence interval (Transparency).

99 percent of the scores lie within 2.58 standard deviations of the mean. Thus we use this knowledge to find a confidence interval.

(0 = standard errors

Example

The mean for watching TV daily is 2.90 with a standard deviation of ( = 2.14, a sample size of N=1940, and a standard error of (0 = .049. Therefore,

Standard Error formula= (0 = (/( N = 2.14 /(1940 = 2.14/44.045 = .049

0 = 2.90

(0 = 0.049

95% standard deviation = 1.96

99% standard deviation = 2.58

95 percent confidence interval = 0 ± 1.96(0

= 2.90 ± 1.96 (.049)

= 2.90 ± .096

= 2.80 to 3.00

Thus the 95 percent confidence interval is between 2.80 and 3.00. The chances are 95 out of 100 that population mean (() lies within this range.

99 percent confidence interval = 0 ± 2.58(0

= 2.90 ± 2.58 (.049)

= 2.90 ± .126

= 2.77 to 3.03

Thus the 99 percent confidence interval is between 2.77 and 3.03. The chances are 99 out of 100 that population mean (() lies within this range.

Statistically significance and significant levels

Statistically significance is to test the probability that a null hypothesis being true is very small (p< .05). Therefore, we reject the null hypothesis and conclude that there is a relationship between the variables under study. And the relationship is existent in the population from which the sample was drawn.

Statistically significance implies that the relationship found in the sample is likely to occur in the population from which the sample was drawn.

Three significant levels:

P< .05 the probability that a null hypothesis being true is small (p< .05).

It implies that the probability that the research hypothesis being true is big (p ( .95).

p< .01 the probability that a null hypothesis being true is small (p< .01).

p ................
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