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# Social Statistics for a Diverse Society / With 3.5" Disk - 97 edition

## ISBN10: 080399026X

Edition: 97
Publisher: Pine Forge Press
Published: 1997
International: No

## ISBN10: 080399026X

#### Other Editions of Social Statistics for a Diverse Society / With 3.5" Disk

1 The What and the Why of Statistics

Introduction
The Research Process
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

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 bYX
Box 8.1 Understanding the Covariance
Calculating bYX 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 (r2) as a PRE Measure
Calculating r
2

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 r2
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 Standard Normal Distribution
The Standard Normal Table
The Structure of the Standard Normal Table
Transforming Z Scores into Proportions (or Percentages)

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
The Dilemma
The Sampling Distribution
The Sampling Distribution of the Mean
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

Calculating the Confidence Interval
Interpreting the Results

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
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: N1 + N2 > 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