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ISBN13: 978-0803990265

ISBN10: 080399026X

Edition: 97

Copyright: 1997

Publisher: Pine Forge Press

Published: 1997

International: No

ISBN10: 080399026X

Edition: 97

Copyright: 1997

Publisher: Pine Forge Press

Published: 1997

International: No

**1 The What and the Why of Statistics**

**Introduction**

**The Research Process**

**Asking Research Questions**

**The Role of Theory**

**Formulating the Hypotheses**

Independent and Dependent Variables: Causality

Independent and Dependent Variables: Guidelines

**Collecting Data**

Levels of Measurement

*Nominal Level of Measurement Ordinal Level of Measurement Interval-Ratio Level of Measurement Cumulative Property of Levels of Measurement Levels of Measurement of Dichotomous Variables*

Discrete and Continuous Variables

**Analyzing Data and Evaluating the Hypotheses**

Descriptive and Inferential Statistics: Principles

Descriptive and Inferential Statistics: Illustration

*Organization of Information: Frequency Distributions Graphic Presentation Measures of Central Tendency Measures of Variability Bivariate Methods Statistical Inference*

Evaluating the Hypotheses

**Looking at Social Differences**

**Box 1.1 A Tale of Simple Arithmetic: How Culture May Influence How We Count**

**Box 1.2 Are You Anxious about Statistics**?

MAIN POINTS

KEY TERMS

SPSS Demonstrations

Exercises

**2 Organization of Information:Frequency Distributions**

**Introduction**

**Frequency Distributions**

**Proportions and Percentages**

**Percentage Distributions**

**Comparisons**

**Statistics in Practice: Labor Force Participation of Native Americans**

**The Construction of Frequency Distributions**

Frequency Distributions for Nominal Variables

Frequency Distributions for Ordinal Level Variables

Frequency Distributions for Interval-Ratio Variables

Box 2.1 Real Limits, Stated Limits, and Midpoints of Class Intervals

**Cumulative Distributions**

**Rates**

**Statistics in Practice: Marriage and Divorce Rates over Time**

**Reading the Research Literature: Statistical Tables**

Basic Principles

Tables with a Different Format

**Conclusion**

MAIN POINTS

KEY TERMS

SPSS Demonstrations

Exercises

**3 Graphic Presentation**

**Introduction**

**The Pie Chart: The Race and Ethnicity of the Elderly**

**The Bar Graph: The Living Arrangements and Labor Force Participation of the**

**Elderly**

**The Statistical Map: The Geographic Distribution of the Elderly**

**The Histogram**

**Statistics in Practice: The "Graying" of America**

**The Frequency Polygon**

**Stem and Leaf Plot**

**Time Series Charts**

**Distortions in Graphs**

**Shrinking and Stretching the Axes: Visual Confusion**

**Distortions with Picture Graphs**

**Statistics in Practice: Diversity at a Glance**

MAIN POINTS

KEY TERMS

SPSS DEMONSTRATIONS

EXERCISES

**4 Measures of Central Tendency**

**Introduction**

**The Mode: Foreign Languages Spoken in the United States**

**The Median: Worries about Health Care**

Finding the Median in Sorted Data

An Odd Number of Cases

An Even Number of Cases

Finding the Median in Frequency Distributions

**Box 4.1 Finding the Median in Grouped Data**

Statistics in Practice: Opinions about National Defense Spending

Statistics in Practice: Changes in Age at First Marriage

Locating Percentiles in Frequency Distributions

**Box 4.2 Finding Percentiles in Grouped Data**

**The Mean: Murder Rates in Fifteen American Cities**

Using a Formula to Calculate the Mean

**Box 4.3 Finding the Mean in a Frequency Distribution**

*Interval-Ratio Level of Measurement*

*Center of Gravity*

*Sensitivity to Extremes*

**The Shape of the Distribution: The Experience of Traumatic Events**

The Symmetrical Distribution

The Positively Skewed Distribution

The Negatively Skewed Distribution

Guidelines for Identifying the Shape of a Distribution

**Considerations for Choosing a Measure of Central Tendency**

Level of Measurement

Skewed Distribution

**Box 4.4 Statistics in Practice: Median Annual Earnings among Subgroups**

Symmetrical Distribution

MAIN POINTS

KEY TERMS

SPSS Demonstrations

Exercises

**5 Measures of Variability**

**Introduction**

**The Importance of Measuring Variability**

**The Index of Qualitative Variation (IQV)**

Steps for Calculating the IQV

*Calculating the Total Number of Differences Calculating the Maximum Possible Differences Computing the Ratio Expressing the IQV as a Percentage Calculating the IQV from Percentage or Proportion Distributions*

**Box 5.1 The IQV Formula: What's Going on Here?**

Statistics in Practice: Diversity in U.S. Society

**Box 5.2 Statistics in Practice: Diversity at Berkeley Through the Year**

**The Range**

**Box 5.3 Using the IQV: American Attitudes about Spending**

**The Interquartile Range: Increases in Elderly Populations**

**The Box Plot**

**The Variance and the Standard Deviation: Changes in the Nursing Home Population**

Calculating the Deviation from the Mean

Calculating the Variance and the Standard Deviation

**Box 5.4 Computational Formula for the Variance and Standard Deviation**

**Considerations for Choosing a Measure of Variation**

**Reading the Research Literature: Gender Differences in Caregiving**

MAIN POINTS

KEY TERMS

**6 Relationships Between Two Variables: Cross-tabulation**

**Introduction**

**Independent and Dependent Variables**

**The Bivariate Table: Safety in Cities**

How to Construct a Bivariate Table: Race and Home Ownership

How to Compute Percentages in a Bivariate Table

*Calculating Percentages within Each Category of the Independent Variable Comparing the Percentages across Different Categories of the Independent Variable*

How to Deal with Ambiguous Relationships Between Variables

**BOX 6.1 Percentaging a Bivariate Table**

**Reading the Research Literature: Medicaid Use among the Elderly**

**The Properties of a Bivariate Relationship**

The Existence of the Relationship

The Strength of the Relationship

The Direction of the Relationship

**Elaboration**

Testing for Nonspuriousness: Firefighters and Property Damage

An Intervening Relationship: Religion and Attitude Toward Abortion

Conditional Relationships: More on Abortion

The Limitations of Elaboration

**Statistics in Practice: Family Support for the Transition from High School**

MAIN POINTS

KEY TERMS

SPSS DEMONSTRATIONS

EXERCISES

**7 Measures of Association for Nominal and Ordinal Variables**

**Introduction**

**Proportionate Reduction of Error**

PRE and Degree of Association

A General Formula for PRE Measures

**Lambda: A Measure of Association for Nominal Variables**

A Method for Calculating Lambda

Statistics in Practice: Home Ownership, Financial Satisfaction, and Race

Some Guidelines for Calculating Lambda

**Gamma and Somers' d: Ordinal Measures of Association**

Analyzing the Association Between Ordinal Variables:

Job Security and Job Satisfaction

*Comparison of Pairs Types of Pairs Uses for Information about Pairs*

Counting Pairs

**Box 7.1 A Martian Eye View of Job Security and Job Satisfaction**

*Same Order Pairs (Ns) Inverse Order Pairs (Nd) Pairs Tied on the Dependent Variable (Nty)*

**Calculating Gamma**

Positive and Negative Gamma

Gamma as a PRE Measure

Statistics in Practice: Trauma by Social Class

**Calculating Somers' d**

Tied Pairs and Somers' d

Somers' d Compared with Gamma

**Using Ordinal Measures of Dichotomous Variables**

**Box 7.2 What Is Strong? What Is Weak? A Guide to Interpretation**

**Reading the Research Literature: Worldview and Abortion Beliefs**

Examining the Data

Interpreting the Data

MAIN POINTS

KEY TERMS

SPSS DEMONSTRATION

EXERCISES

**8 Bivariate Regression and Correlation**

**Introduction**

**The Scatter Diagram**

**Linear Relations and Prediction Rules**

Constructing Straight Line Graphs

Finding the Best-Fitting Line

*Defining Error The Sum of Squared Error (Se2) The Least-Squares Line Review*

Computing* a* and** ***b* for the Prediction Equation

Interpreting a and* b*_{YX}

**Box 8.1 Understanding the Covariance**

Calculating *b*_{YX} Using a Computational Formula

**Box 8.2 A Note of Nonlinear Relationships**

**Statistics in Practice: GNP and Willingness to Volunteer Time for**

**Environmental Protection**

**Methods for Assessing the Accuracy of Predictions**

Prediction Errors

*The Coefficient of Determination (r*^{2}*) as a PRE Measure Calculating r*

Pearson's Correlation Coefficient (r)

*Characteristics of Pearson's r Calculating r Using a Computational Formula*

**Statistics in Practice: Comparable Worth Discrimination**

Computing a and b for the Prediction Equation

Computing r and *r*^{2}

**Statistics in Practice: The Marriage Penalty in Earnings**

MAIN POINTS

KEY TERMS

SPSS DEMONSTRATIONS

EXERCISES

**9 Organization of Information and Measurement of Relationships: A Review of Descriptive Data Analysis**

**Introduction**

**Descriptive Data Analysis for Nominal Variables**

Statistics in Practice: Gender and Local Political Party Activism

*Organize the Data into a Frequency Distribution Display the Data in a Graph Describe What Is Typical of a Distribution Describe Variability Within a Distribution Describe the Relationship Between Two Variables*

**Descriptive Data Analysis for Ordinal Variables**

Gender and Local Political Party Activism: Continuing Our Research Example

*Organize the Data into a Frequency Distribution Display the Data in a Graph Describe What Is Typical of a Distribution Describe Variability Within a Distribution Describe the Relationship Between Two Variables*

**Descriptive Data Analysis for Interval-Ratio Variables**

Statistics in Practice: Education and Income

*Organize the Data into a Frequency Distribution Display the Data in a Graph Describe What Is Typical of a Distribution Describe Variability Within a Distribution Describe the Relationship Between Two Variables*

**A Final Note**

Exercises

**10 The Normal Distribution**

**Introduction**

**Properties of the Normal Distribution**

Empirical Distributions Approximating the Normal Distribution

An Example: Final Grades in Statistics

Areas Under the Normal Curve

Interpreting the Standard Deviation

**Standard (Z) Scores**

Transforming a Raw Score into a Z Score* *Transforming a Z Score into a Raw Score

The Structure of the Standard Normal Table

*Finding the Area Between the Mean and a Specified Positive Z Score Finding the Area Between the Mean and a Specified Negative Z Score Finding the Area Between Two Z Scores on the Same Side of the Mean Finding the Area Between Two Z Scores on Opposite Sides of the Mean Finding the Area Above a Positive Z Score or Below a Negative Z Score*

Transforming Proportions (or Percentages) into Z Scores

*Finding a Z Score Bounding an Area Above It Finding a Z Score Bounding an Area Below It*

Working with Percentiles

*Finding the Percentile Rank of a Score Higher Than the Mean Finding the Percentile Rank of a Score Lower Than the Mean Finding the Raw Score Associated with a Percentile Higher Than 50 Finding the Raw Score Associated with a Percentile Lower Than 50*

**A Final Note**

MAIN POINTS

KEY TERMS

SPSS Demonstrations

Exercises

**11 Building Blocks Of Inference: Sampling And Sampling**

**Introduction**

**Aims of Sampling**

**Some Basic Principles of Probability**

**Probability Sampling**

The Simple Random Sample

Systematic Random Sample

Stratified Random Sampling

**Box 11.1 Disproportionate Stratified Samples and Diversity**

**The Concept of Sampling Distribution**

The Population* *The Sample

An Illustration

Review

*The Population The Sample The Sampling Distribution of the Mean*

The Mean of the Sampling Distribution

The Standard Error of the Mean

**The Central Limit Theorem**

The Size of the Sample

The Significance of the Sampling Distribution and the Central Limit Theorem

MAIN POINTS

KEY TERMS

SPSS Demonstration

Exercises

**12 Estimation**

**Introduction**

**Estimation Defined**

Reasons for Estimation

Point and Interval Estimation

**Confidence Intervals for Means**

Rationale for Confidence Intervals

**Box 12.1 Estimation a Type of Inference**

Procedures for Estimating Means

*Calculating the Standard Error of the Mean Deciding on the Level of Confidence and Finding the Corresponding Z Value Calculating the Confidence Interval Interpreting the Results*

Reducing Risk

**Estimating Sigma**

*Calculating the Standard Error of the Mean Deciding on the Level of Confidence and Finding the Corresponding Z Value*

**Sample Size and Confidence Intervals**

**Box 12.2 What Affects Confidence Interval Width?A Summary**

**Statistics in Practice: Hispanic Migration and Earnings**

**Confidence Intervals for Proportions**

The Sampling Distribution of Proportions

Procedures for Estimating Proportions

*Calculating the Standard Error of the Proportion Deciding on the Desired Level of Confidence and Finding the Corresponding Z Value Calculating the Confidence Interval Interpreting the Results*

Increasing the Sample Size

Example #3 Revisited: Raising the Minimum Wage

*Calculating the Standard Error of the Proportion*

*Deciding on the Desired Level of Confidence and Finding the Corresponding Z Value*

*Calculating the Confidence Interval*

*Interpreting the Results*

**Statistics in Practice: Opinions about the Death Penalty**

**Statistics in Practice: More on the Death Penalty**

*Calculating the Standard Error of the Mean*

*Deciding on the Level of Confidence and Finding the Corresponding Z Value*

*Calculating the Confidence Interval*

*Interpreting the Results*

MAIN POINTS

KEY TERMS

SPSS Demonstration

Exercises

**13 Testing Hypotheses: The Basics**

**Introduction**

**Elements of Statistical Hypothesis Testing**

The Research Hypothesis (H1)

The Null Hypothesis (H0)

Assumptions of Statistical Hypothesis Testing

The Test Statistic and the P Value

Determining What Is Sufficiently Improbable

The Critical Value of the Test Statistic

One- and Two-Tailed Tests

Making a Decision and Interpreting the Result

The Six Steps in Hypothesis Testing: A Summary

*Making Assumptions Stating the Research and the Null Hypotheses Selecting the Sampling Distribution and Specifying the Test Statistic Choosing Alpha and Establishing the Region of Rejection Computing the Test Statistics Making a Decision and Interpreting the Results *Statistics in Practice: The Earnings of White Women

*Applying the Six-Step Model*

*Comparing One- and Two-Tailed Tests*

**Errors in Hypothesis Testing**

MAIN POINTS

KEY TERMS

**14 Testing Hypotheses about Two Samples**

**Introduction**

**The Structure of Hypothesis Testing with Two Samples**

The Assumption of Independent Samples

Stating the Research and the Null Hypotheses

**The Sampling Distribution of the Difference Between Means**

**Estimating the Standard Error**

**The t Statistic**

**Calculating the Estimated Standard Error**

The Population Variances Are Assumed Equal

The Population Variances Are Assumed Unequal

**Comparing the t and the Z Statistics**

**The t Distribution and the Degrees of Freedom (df)**

Determining the Degrees of Freedom

Adjusting for Unequal Variances

The Shape of the t Distribution

Critical Values of the t Distribution

**Review**

Hypotheses about Differences Between Means: Illustrations

The Population Variances Are Assumed Equal: The Earnings of Asian American Men

The Population Variances Are Assumed Unequal: Ratings of Ross Perot

**Testing the Significance of the Difference Between Two Sample Proportions (with Large Samples: N**_{1}** + N**_{2}** > 100)**

An Illustration: Public Opinion about the Environment

Statistics in Practice: Gender and Abortion Attitudes

**Reading the Research Literature: Reporting the Results of Statistical Hypothesis Testing**

MAIN POINTS

KEY TERMS

SPSS DEMONSTRATIONS

EXCERCISES

SPSS PROBLEMS

GROUP PROBLEMS

**15 The Chi-Square Test**

**Introduction**

**The Concept of Chi-Square as a Statistical Test**

The Concept of Statistical Independence

The Structure of Hypothesis Testing with Chi-Square

*The Assumptions*

*Stating the Research and the Null Hypotheses*

*The Concept of Expected Frequencies*

*Calculating the Expected Frequencies*

*Calculating the Obtained Chi-Square*

*The Sampling Distribution of Chi-Square*

*Determining the Degrees of Freedom*

*Critical Values of the Chi-Square Distribution*

Review

**The Limitations of the Chi-Square Test: Sample Size and Statistical Significance**

**Box 15.1 Comparing Chi-Square with Tests of Differences Between Proportions**

**Statistics in Practice: Social Class and Health**

**Reading the Research Literature: AIDS Risks among Women**

MAIN POINTS

KEY TERMS

SPSS DEMONSTRATION

EXERCISES

**16 Reviewing Inferential Statistics**

**Introduction**

**Normal Distributions**

**Sampling: The Case of AIDS**

**Estimation**

Statistics in Practice: The War on Drugs

**Box 16.1 Interval Estimation for Peers as a Major Influence on the Drug Attitudes of the Young**

The Process of Statistical Hypothesis Testing

Step 1: Making Assumptions

Step 2: Stating the Research and the Null Hypotheses

Step 3: Selecting a Sampling Distribution and a Test Statistic

Step 4: Choosing Alpha and Establishing the Region of Rejection

**Box 16.2 Possible Hypotheses for Comparing Two Samples**

**Box 16.3 Criteria for Statistical Tests When Comparing Two Samples**

*Finding the Critical Value of Z Finding the Critical Value of t Finding the Critical Value of Chi-Square*

Step 5: Computing the Test Statistic

Step 6: Making a Decision and Interpreting the Results

**Statistics in Practice: Affirmative Action**

**Box 16.4 Formulas for Z, t, and c2**

**Box 16.5 Affirmative Action: The Process of Statistical Hypothesis Testing, Using a Z test for Proportions**

**Statistics in Practice: Attitudes Toward Illegal Immigrants**

**Box 16.6 Attitudes Toward Illegal Immigrants: The Process of Statistical Hypothesis Testing, Using a t Test**

**Statistics in Practice: Education and Employment**

Sampling Technique and Sample Characteristics

Comparing Ratings of the Major Between Sociology and Other Social Science Alumni

Ratings of Foundational Skills in Sociology: Changes Over Time

**Box 16.7 Education and Employment: The Process of Statistical Hypothesis Testing, Using Chi-Square**

Gender Differences in Ratings of Foundational Skills, Occupational

Prestige, and Income

**Box 16.8 Occupational Prestige of Male and Female Sociology Alumni: The Process of Statistical Hypothesis Testing, Using a ****t ****Test**

**Conclusion**

Exercises

1 The What and Why of Statistics

2 Organization of Information: Frequency Distributions

3 Graphic Presentation

4 Measures of Central Tendency

5 Measures of Variability

6 Relationships Between Two Variables: Cross-tabulation

7 Measures of Association for Nominal and Ordinal Variables

8 Bivariate Regression and Correlation

9 Organization of Information and Measurement of Relationships: A Review of Descriptive Data Analysis

10 The Normal Distribution

11 Building Blocks of Inference: Sampling and Sampling Distributions

12 Estimation

13 Testing Hypotheses: The Basics

14 Testing Hypotheses About Two Samples

15 The Chi-Square Test

16 Reviewing Inferential Statistics

Appendix A, Table of Random Numbers; Appendix B, The Standard Normal Table; Appendix C, Distribution of t; Appendix D, Distribution of Chi-Square; Appendix E, How to Use the Statistical Package; Appendix F, The General Social Survey; Appendix G, How to Use the GSS Data Files and LotusScreenCam

References

Glossary/Index

ISBN10: 080399026X

Edition: 97

Copyright: 1997

Publisher: Pine Forge Press

Published: 1997

International: No

Table of Contents

**1 The What and the Why of Statistics**

**Introduction**

**The Research Process**

**Asking Research Questions**

**The Role of Theory**

**Formulating the Hypotheses**

Independent and Dependent Variables: Causality

Independent and Dependent Variables: Guidelines

**Collecting Data**

Levels of Measurement

*Nominal Level of Measurement Ordinal Level of Measurement Interval-Ratio Level of Measurement Cumulative Property of Levels of Measurement Levels of Measurement of Dichotomous Variables*

Discrete and Continuous Variables

**Analyzing Data and Evaluating the Hypotheses**

Descriptive and Inferential Statistics: Principles

Descriptive and Inferential Statistics: Illustration

*Organization of Information: Frequency Distributions Graphic Presentation Measures of Central Tendency Measures of Variability Bivariate Methods Statistical Inference*

Evaluating the Hypotheses

**Looking at Social Differences**

**Box 1.1 A Tale of Simple Arithmetic: How Culture May Influence How We Count**

**Box 1.2 Are You Anxious about Statistics**?

MAIN POINTS

KEY TERMS

SPSS Demonstrations

Exercises

**2 Organization of Information:Frequency Distributions**

**Introduction**

**Frequency Distributions**

**Proportions and Percentages**

**Percentage Distributions**

**Comparisons**

**Statistics in Practice: Labor Force Participation of Native Americans**

**The Construction of Frequency Distributions**

Frequency Distributions for Nominal Variables

Frequency Distributions for Ordinal Level Variables

Frequency Distributions for Interval-Ratio Variables

Box 2.1 Real Limits, Stated Limits, and Midpoints of Class Intervals

**Cumulative Distributions**

**Rates**

**Statistics in Practice: Marriage and Divorce Rates over Time**

**Reading the Research Literature: Statistical Tables**

Basic Principles

Tables with a Different Format

**Conclusion**

MAIN POINTS

KEY TERMS

SPSS Demonstrations

Exercises

**3 Graphic Presentation**

**Introduction**

**The Pie Chart: The Race and Ethnicity of the Elderly**

**The Bar Graph: The Living Arrangements and Labor Force Participation of the**

**Elderly**

**The Statistical Map: The Geographic Distribution of the Elderly**

**The Histogram**

**Statistics in Practice: The "Graying" of America**

**The Frequency Polygon**

**Stem and Leaf Plot**

**Time Series Charts**

**Distortions in Graphs**

**Shrinking and Stretching the Axes: Visual Confusion**

**Distortions with Picture Graphs**

**Statistics in Practice: Diversity at a Glance**

MAIN POINTS

KEY TERMS

SPSS DEMONSTRATIONS

EXERCISES

**4 Measures of Central Tendency**

**Introduction**

**The Mode: Foreign Languages Spoken in the United States**

**The Median: Worries about Health Care**

Finding the Median in Sorted Data

An Odd Number of Cases

An Even Number of Cases

Finding the Median in Frequency Distributions

**Box 4.1 Finding the Median in Grouped Data**

Statistics in Practice: Opinions about National Defense Spending

Statistics in Practice: Changes in Age at First Marriage

Locating Percentiles in Frequency Distributions

**Box 4.2 Finding Percentiles in Grouped Data**

**The Mean: Murder Rates in Fifteen American Cities**

Using a Formula to Calculate the Mean

**Box 4.3 Finding the Mean in a Frequency Distribution**

*Interval-Ratio Level of Measurement*

*Center of Gravity*

*Sensitivity to Extremes*

**The Shape of the Distribution: The Experience of Traumatic Events**

The Symmetrical Distribution

The Positively Skewed Distribution

The Negatively Skewed Distribution

Guidelines for Identifying the Shape of a Distribution

**Considerations for Choosing a Measure of Central Tendency**

Level of Measurement

Skewed Distribution

**Box 4.4 Statistics in Practice: Median Annual Earnings among Subgroups**

Symmetrical Distribution

MAIN POINTS

KEY TERMS

SPSS Demonstrations

Exercises

**5 Measures of Variability**

**Introduction**

**The Importance of Measuring Variability**

**The Index of Qualitative Variation (IQV)**

Steps for Calculating the IQV

*Calculating the Total Number of Differences Calculating the Maximum Possible Differences Computing the Ratio Expressing the IQV as a Percentage Calculating the IQV from Percentage or Proportion Distributions*

**Box 5.1 The IQV Formula: What's Going on Here?**

Statistics in Practice: Diversity in U.S. Society

**Box 5.2 Statistics in Practice: Diversity at Berkeley Through the Year**

**The Range**

**Box 5.3 Using the IQV: American Attitudes about Spending**

**The Interquartile Range: Increases in Elderly Populations**

**The Box Plot**

**The Variance and the Standard Deviation: Changes in the Nursing Home Population**

Calculating the Deviation from the Mean

Calculating the Variance and the Standard Deviation

**Box 5.4 Computational Formula for the Variance and Standard Deviation**

**Considerations for Choosing a Measure of Variation**

**Reading the Research Literature: Gender Differences in Caregiving**

MAIN POINTS

KEY TERMS

**6 Relationships Between Two Variables: Cross-tabulation**

**Introduction**

**Independent and Dependent Variables**

**The Bivariate Table: Safety in Cities**

How to Construct a Bivariate Table: Race and Home Ownership

How to Compute Percentages in a Bivariate Table

*Calculating Percentages within Each Category of the Independent Variable Comparing the Percentages across Different Categories of the Independent Variable*

How to Deal with Ambiguous Relationships Between Variables

**BOX 6.1 Percentaging a Bivariate Table**

**Reading the Research Literature: Medicaid Use among the Elderly**

**The Properties of a Bivariate Relationship**

The Existence of the Relationship

The Strength of the Relationship

The Direction of the Relationship

**Elaboration**

Testing for Nonspuriousness: Firefighters and Property Damage

An Intervening Relationship: Religion and Attitude Toward Abortion

Conditional Relationships: More on Abortion

The Limitations of Elaboration

**Statistics in Practice: Family Support for the Transition from High School**

MAIN POINTS

KEY TERMS

SPSS DEMONSTRATIONS

EXERCISES

**7 Measures of Association for Nominal and Ordinal Variables**

**Introduction**

**Proportionate Reduction of Error**

PRE and Degree of Association

A General Formula for PRE Measures

**Lambda: A Measure of Association for Nominal Variables**

A Method for Calculating Lambda

Statistics in Practice: Home Ownership, Financial Satisfaction, and Race

Some Guidelines for Calculating Lambda

**Gamma and Somers' d: Ordinal Measures of Association**

Analyzing the Association Between Ordinal Variables:

Job Security and Job Satisfaction

*Comparison of Pairs Types of Pairs Uses for Information about Pairs*

Counting Pairs

**Box 7.1 A Martian Eye View of Job Security and Job Satisfaction**

*Same Order Pairs (Ns) Inverse Order Pairs (Nd) Pairs Tied on the Dependent Variable (Nty)*

**Calculating Gamma**

Positive and Negative Gamma

Gamma as a PRE Measure

Statistics in Practice: Trauma by Social Class

**Calculating Somers' d**

Tied Pairs and Somers' d

Somers' d Compared with Gamma

**Using Ordinal Measures of Dichotomous Variables**

**Box 7.2 What Is Strong? What Is Weak? A Guide to Interpretation**

**Reading the Research Literature: Worldview and Abortion Beliefs**

Examining the Data

Interpreting the Data

MAIN POINTS

KEY TERMS

SPSS DEMONSTRATION

EXERCISES

**8 Bivariate Regression and Correlation**

**Introduction**

**The Scatter Diagram**

**Linear Relations and Prediction Rules**

Constructing Straight Line Graphs

Finding the Best-Fitting Line

*Defining Error The Sum of Squared Error (Se2) The Least-Squares Line Review*

Computing* a* and** ***b* for the Prediction Equation

Interpreting a and* b*_{YX}

**Box 8.1 Understanding the Covariance**

Calculating *b*_{YX} Using a Computational Formula

**Box 8.2 A Note of Nonlinear Relationships**

**Statistics in Practice: GNP and Willingness to Volunteer Time for**

**Environmental Protection**

**Methods for Assessing the Accuracy of Predictions**

Prediction Errors

*The Coefficient of Determination (r*^{2}*) as a PRE Measure Calculating r*

Pearson's Correlation Coefficient (r)

*Characteristics of Pearson's r Calculating r Using a Computational Formula*

**Statistics in Practice: Comparable Worth Discrimination**

Computing a and b for the Prediction Equation

Computing r and *r*^{2}

**Statistics in Practice: The Marriage Penalty in Earnings**

MAIN POINTS

KEY TERMS

SPSS DEMONSTRATIONS

EXERCISES

**9 Organization of Information and Measurement of Relationships: A Review of Descriptive Data Analysis**

**Introduction**

**Descriptive Data Analysis for Nominal Variables**

Statistics in Practice: Gender and Local Political Party Activism

Display the Data in a Graph

Describe What Is Typical of a Distribution

Describe Variability Within a Distribution

Describe the Relationship Between Two Variables

**Descriptive Data Analysis for Ordinal Variables**

Gender and Local Political Party Activism: Continuing Our Research Example

Display the Data in a Graph

Describe What Is Typical of a Distribution

Describe Variability Within a Distribution

Describe the Relationship Between Two Variables

**Descriptive Data Analysis for Interval-Ratio Variables**

Statistics in Practice: Education and Income

Display the Data in a Graph

Describe What Is Typical of a Distribution

Describe Variability Within a Distribution

Describe the Relationship Between Two Variables

**A Final Note**

Exercises

**10 The Normal Distribution**

**Introduction**

**Properties of the Normal Distribution**

Empirical Distributions Approximating the Normal Distribution

An Example: Final Grades in Statistics

Areas Under the Normal Curve

Interpreting the Standard Deviation

**Standard (Z) Scores**

Transforming a Raw Score into a Z Score* *Transforming a Z Score into a Raw Score

The Structure of the Standard Normal Table

*Finding the Area Between the Mean and a Specified Positive Z Score Finding the Area Between the Mean and a Specified Negative Z Score Finding the Area Between Two Z Scores on the Same Side of the Mean Finding the Area Between Two Z Scores on Opposite Sides of the Mean Finding the Area Above a Positive Z Score or Below a Negative Z Score*

Transforming Proportions (or Percentages) into Z Scores

*Finding a Z Score Bounding an Area Above It Finding a Z Score Bounding an Area Below It*

Working with Percentiles

*Finding the Percentile Rank of a Score Higher Than the Mean Finding the Percentile Rank of a Score Lower Than the Mean Finding the Raw Score Associated with a Percentile Higher Than 50 Finding the Raw Score Associated with a Percentile Lower Than 50*

**A Final Note**

MAIN POINTS

KEY TERMS

SPSS Demonstrations

Exercises

**11 Building Blocks Of Inference: Sampling And Sampling**

**Introduction**

**Aims of Sampling**

**Some Basic Principles of Probability**

**Probability Sampling**

The Simple Random Sample

Systematic Random Sample

Stratified Random Sampling

**Box 11.1 Disproportionate Stratified Samples and Diversity**

**The Concept of Sampling Distribution**

The Population* *The Sample

An Illustration

Review

*The Population The Sample The Sampling Distribution of the Mean*

The Mean of the Sampling Distribution

The Standard Error of the Mean

**The Central Limit Theorem**

The Size of the Sample

The Significance of the Sampling Distribution and the Central Limit Theorem

MAIN POINTS

KEY TERMS

SPSS Demonstration

Exercises

**12 Estimation**

**Introduction**

**Estimation Defined**

Reasons for Estimation

Point and Interval Estimation

**Confidence Intervals for Means**

Rationale for Confidence Intervals

**Box 12.1 Estimation a Type of Inference**

Procedures for Estimating Means

*Calculating the Standard Error of the Mean Deciding on the Level of Confidence and Finding the Corresponding Z Value Calculating the Confidence Interval Interpreting the Results*

Reducing Risk

**Estimating Sigma**

*Calculating the Standard Error of the Mean Deciding on the Level of Confidence and Finding the Corresponding Z Value*

**Sample Size and Confidence Intervals**

**Box 12.2 What Affects Confidence Interval Width?A Summary**

**Statistics in Practice: Hispanic Migration and Earnings**

**Confidence Intervals for Proportions**

The Sampling Distribution of Proportions

Procedures for Estimating Proportions

*Calculating the Standard Error of the Proportion Deciding on the Desired Level of Confidence and Finding the Corresponding Z Value Calculating the Confidence Interval Interpreting the Results*

Increasing the Sample Size

Example #3 Revisited: Raising the Minimum Wage

*Calculating the Standard Error of the Proportion*

*Deciding on the Desired Level of Confidence and Finding the Corresponding Z Value*

*Calculating the Confidence Interval*

*Interpreting the Results*

**Statistics in Practice: Opinions about the Death Penalty**

**Statistics in Practice: More on the Death Penalty**

*Calculating the Standard Error of the Mean*

*Deciding on the Level of Confidence and Finding the Corresponding Z Value*

*Calculating the Confidence Interval*

*Interpreting the Results*

MAIN POINTS

KEY TERMS

SPSS Demonstration

Exercises

**13 Testing Hypotheses: The Basics**

**Introduction**

**Elements of Statistical Hypothesis Testing**

The Research Hypothesis (H1)

The Null Hypothesis (H0)

Assumptions of Statistical Hypothesis Testing

The Test Statistic and the P Value

Determining What Is Sufficiently Improbable

The Critical Value of the Test Statistic

One- and Two-Tailed Tests

Making a Decision and Interpreting the Result

The Six Steps in Hypothesis Testing: A Summary

*Making Assumptions Stating the Research and the Null Hypotheses Selecting the Sampling Distribution and Specifying the Test Statistic Choosing Alpha and Establishing the Region of Rejection Computing the Test Statistics Making a Decision and Interpreting the Results *Statistics in Practice: The Earnings of White Women

*Applying the Six-Step Model*

*Comparing One- and Two-Tailed Tests*

**Errors in Hypothesis Testing**

MAIN POINTS

KEY TERMS

**14 Testing Hypotheses about Two Samples**

**Introduction**

**The Structure of Hypothesis Testing with Two Samples**

The Assumption of Independent Samples

Stating the Research and the Null Hypotheses

**The Sampling Distribution of the Difference Between Means**

**Estimating the Standard Error**

**The t Statistic**

**Calculating the Estimated Standard Error**

The Population Variances Are Assumed Equal

The Population Variances Are Assumed Unequal

**Comparing the t and the Z Statistics**

**The t Distribution and the Degrees of Freedom (df)**

Determining the Degrees of Freedom

Adjusting for Unequal Variances

The Shape of the t Distribution

Critical Values of the t Distribution

**Review**

Hypotheses about Differences Between Means: Illustrations

The Population Variances Are Assumed Equal: The Earnings of Asian American Men

The Population Variances Are Assumed Unequal: Ratings of Ross Perot

**Testing the Significance of the Difference Between Two Sample Proportions (with Large Samples: N**_{1}** + N**_{2}** > 100)**

An Illustration: Public Opinion about the Environment

Statistics in Practice: Gender and Abortion Attitudes

**Reading the Research Literature: Reporting the Results of Statistical Hypothesis Testing**

MAIN POINTS

KEY TERMS

SPSS DEMONSTRATIONS

EXCERCISES

SPSS PROBLEMS

GROUP PROBLEMS

**15 The Chi-Square Test**

**Introduction**

**The Concept of Chi-Square as a Statistical Test**

The Concept of Statistical Independence

The Structure of Hypothesis Testing with Chi-Square

*The Assumptions*

*Stating the Research and the Null Hypotheses*

*The Concept of Expected Frequencies*

*Calculating the Expected Frequencies*

*Calculating the Obtained Chi-Square*

*The Sampling Distribution of Chi-Square*

*Determining the Degrees of Freedom*

*Critical Values of the Chi-Square Distribution*

Review

**The Limitations of the Chi-Square Test: Sample Size and Statistical Significance**

**Box 15.1 Comparing Chi-Square with Tests of Differences Between Proportions**

**Statistics in Practice: Social Class and Health**

**Reading the Research Literature: AIDS Risks among Women**

MAIN POINTS

KEY TERMS

SPSS DEMONSTRATION

EXERCISES

**16 Reviewing Inferential Statistics**

**Introduction**

**Normal Distributions**

**Sampling: The Case of AIDS**

**Estimation**

Statistics in Practice: The War on Drugs

**Box 16.1 Interval Estimation for Peers as a Major Influence on the Drug Attitudes of the Young**

The Process of Statistical Hypothesis Testing

Step 1: Making Assumptions

Step 2: Stating the Research and the Null Hypotheses

Step 3: Selecting a Sampling Distribution and a Test Statistic

Step 4: Choosing Alpha and Establishing the Region of Rejection

**Box 16.2 Possible Hypotheses for Comparing Two Samples**

**Box 16.3 Criteria for Statistical Tests When Comparing Two Samples**

*Finding the Critical Value of Z Finding the Critical Value of t Finding the Critical Value of Chi-Square*

Step 5: Computing the Test Statistic

Step 6: Making a Decision and Interpreting the Results

**Statistics in Practice: Affirmative Action**

**Box 16.4 Formulas for Z, t, and c2**

**Box 16.5 Affirmative Action: The Process of Statistical Hypothesis Testing, Using a Z test for Proportions**

**Statistics in Practice: Attitudes Toward Illegal Immigrants**

**Box 16.6 Attitudes Toward Illegal Immigrants: The Process of Statistical Hypothesis Testing, Using a t Test**

**Statistics in Practice: Education and Employment**

Sampling Technique and Sample Characteristics

Comparing Ratings of the Major Between Sociology and Other Social Science Alumni

Ratings of Foundational Skills in Sociology: Changes Over Time

**Box 16.7 Education and Employment: The Process of Statistical Hypothesis Testing, Using Chi-Square**

Gender Differences in Ratings of Foundational Skills, Occupational

Prestige, and Income

**Box 16.8 Occupational Prestige of Male and Female Sociology Alumni: The Process of Statistical Hypothesis Testing, Using a ****t ****Test**

**Conclusion**

Exercises

1 The What and Why of Statistics

2 Organization of Information: Frequency Distributions

3 Graphic Presentation

4 Measures of Central Tendency

5 Measures of Variability

6 Relationships Between Two Variables: Cross-tabulation

7 Measures of Association for Nominal and Ordinal Variables

8 Bivariate Regression and Correlation

9 Organization of Information and Measurement of Relationships: A Review of Descriptive Data Analysis

10 The Normal Distribution

11 Building Blocks of Inference: Sampling and Sampling Distributions

12 Estimation

13 Testing Hypotheses: The Basics

14 Testing Hypotheses About Two Samples

15 The Chi-Square Test

16 Reviewing Inferential Statistics

Appendix A, Table of Random Numbers; Appendix B, The Standard Normal Table; Appendix C, Distribution of t; Appendix D, Distribution of Chi-Square; Appendix E, How to Use the Statistical Package; Appendix F, The General Social Survey; Appendix G, How to Use the GSS Data Files and LotusScreenCam

References

Glossary/Index

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