The Statistical Imagination: Elementary Statistics for the Social Sciences / Edition 2

by Ferris Ritchey

Overview

This basic social science statistics text uses illustrations and exercises for sociology, social work, political science, and criminal justice. Praised for a writing style that takes the anxiety out of statistics courses, the author explains basic statistical principles through a variety of engaging exercises, each designed to illuminate the unique theme of examining society both creatively and logically. In an effort to make the study of statistics relevant to students of the social sciences, the author encourages readers to interpret the results of calculations in the context of more substantive social issues, while continuing to value precise and accurate research.

Product Details

ISBN-13:	9780072943047
Publisher:	McGraw-Hill Higher Education
Publication date:	01/26/2007
Edition description:	New Edition
Pages:	672
Product dimensions:	7.60(w) x 9.30(h) x 1.20(d)

About the Author

Ferris J. Ritchey is an Associate Professor in the Department of Sociology at the University of Alabama at Birmingham. He has been teaching undergraduate and graduate statistics courses for over 20 years. He has published in leading journals in the field including the Journal of Health and Social Behavior, Medical Care, and the American Journal of Public Health, and has consulted and/or served on panels with the center for Disease Control, the U.S. Census Bureau, and the National Institutes of Mental Health. Professor Ritchey was the School of Social Sciences recipient of the 1995 President’s Award for Excellence in Teaching at University of Alabama.

Table of Contents

Preface     X
The Statistical Imagination     1
Introduction     1
The Statistical Imagination     3
Linking the Statistical Imagination to the Sociological Imagination     4
Statistical Norms and Social Norms     4
Statistical Ideals and Social Values     5
Statistics and Science: Tools for Proportional Thinking     7
Descriptive and Inferential Statistics     7
What Is Science?     8
Scientific Skepticism and the Statistical Imagination     9
Conceiving of Data     10
The Research Process     13
Proportional Thinking: Calculating Proportions, Percentages, and Rates     15
How to Succeed in This Course and Enjoy It     20
Statistical Follies and Fallacies: The Problem of Small Denominators     21
Organizing Data to Minimize Statistical Error     36
Introduction     36
Controlling Sampling Error     37
Careful Statistical Estimation versus Hasty Guesstimation     40
Sampling Error and Its Management with Probability Theory     41
Controlling Measurement Error     42
Levels of Measurement: Careful Selection of Statistical Procedures     42
Measurement     42
Nominal Variables     43
Ordinal Variables     44
Interval Variables     44
Ratio Variables     45
Improving the Level of Measurement     47
Distinguishing Level of Measurement and Unit of Measure     47
Coding and Counting Observations     48
Frequency Distributions     50
Standardizing Score Distributions     51
Coding and Counting Interval/Ratio Data     52
Rounding Interval/Ratio Observations     53
The Real Limits of Rounded Scores     53
Proportional and Percentage Frequency Distributions for Interval/Ratio Variables     55
Cumulative Percentage Frequency Distributions     56
Percentiles and Quartiles     58
Grouping Interval/Ratio Data     60
Statistical Follies and Fallacies: The Importance of Having a Representative Sample     61
Charts and Graphs: A Picture Says a Thousand Words     78
Introduction: Pictorial Presentation of Data     78
Graphing and Table Construction Guidelines     79
Graphing Nominal/Ordinal Data     80
Pie Charts     80
Bar Charts     83
Graphing Interval/Ratio Variables      86
Histograms     86
Polygons and Line Graphs     89
Using Graphs with Inferential Statistics and Research Applications     93
Statistical Follies and Fallacies: Graphical Distortion     94
Measuring Averages     107
Introduction     107
The Mean     108
Proportional Thinking about the Mean     109
Potential Weaknesses of the Mean: Situations Where Reporting It Alone May Mislead     111
The Median     112
Potential Weaknesses of the Median: Situations Where Reporting It Alone May Mislead     114
The Mode     115
Potential Weaknesses of the Mode: Situations Where Reporting It Alone May Mislead     116
Central Tendency Statistics and the Appropriate Level of Measurement     117
Frequency Distribution Curves: Relationships Among the Mean, Median, and Mode     118
The Normal Distribution     118
Skewed Distributions     119
Using Sample Data to Estimate the Shape of a Score Distribution in a Population     120
Organizing Data for Calculating Central Tendency Statistics     122
Spreadsheet Format for Calculating Central Tendency Statistics     122
Frequency Distribution Format for Calculating the Mode     123
Statistical Follies and Fallacies: Mixing Subgroups in the Calculation of the Mean     124
Measuring Dispersion or Spread in a Distribution of Scores     136
Introduction     136
The Range     138
Limitations of the Range: Situations Where Reporting It Alone May Mislead     139
The Standard Deviation     139
Proportional and Linear Thinking about the Standard Deviation     140
Limitations of the Standard Deviation     145
The Standard Deviation as an Integral Part of Inferential Statistics     147
Why Is It Called the "Standard" Deviation?     148
Standardized Scores (Z-Scores)     148
The Standard Deviation and the Normal Distribution     150
Tabular Presentation of Results     153
Statistical Follies and Fallacies: What Does It Indicate When the Standard Deviation Is Larger than the Mean?     154
Probability Theory and the Normal Probability Distribution     168
Introduction: The Human Urge to Predict the Future     168
What Is a Probability?     170
Basic Rules of Probability Theory     172
Probabilities Always Range Between 0 and 1     172
The Addition Rule for Alternative Events     172
Adjust for Joint Occurrences     173
The Multiplication Rule for Compound Events     174
Account for Replacement with Compound Events     174
Using the Normal Curve as a Probability Distribution     176
Proportional Thinking about a Group of Cases and Single Cases     176
Partitioning Areas Under the Normal Curve     179
Sample Problems Using the Normal Curve     181
Computing Percentiles for Normally Distributed Populations     191
The Normal Curve as a Tool for Proportional Thinking     193
Statistical Follies and Fallacies: The Gambler's Fallacy: Independence of Probability Events     194
Using Probability Theory to Produce Sampling Distributions     206
Introduction: Estimating Parameters     206
Point Estimates     207
Predicting Sampling Error     207
Sampling Distributions     209
Sampling Distributions for Interval/Ratio Variables     209
The Standard Error     211
The Law of Large Numbers     212
The Central Limit Theorem     212
Sampling Distributions for Nominal Variables     215
Rules Concerning a Sampling Distribution of Proportions     218
Bean Counting as a Way of Grasping the Statistical Imagination     219
Distinguishing Among Populations, Samples, and Sampling Distributions     221
Statistical Follies and Fallacies: Treating a Point Estimate as Though It Were Absolutely True     222
Parameter Estimation Using Confidence Intervals     237
Introduction     237
Confidence Interval of a Population Mean     240
Calculating the Standard Error for a Confidence Interval of a Population Mean     241
Choosing the Critical Z-Score, Z[subscript Alpha]     242
Calculating the Error Term     243
Calculating the Confidence Interval     243
The Five Steps for Computing a Confidence Interval of a Population Mean, Mu[subscript x]     245
Proper Interpretation of Confidence Intervals     247
Common Misinterpretations of Confidence Intervals     249
The Chosen Level of Confidence and the Precision of the Confidence Interval     249
Sample Size and the Precision of the Confidence Interval     250
Large-Sample Confidence Interval of a Population Proportion     252
Choosing a Sample Size for Polls, Surveys, and Research Studies     256
Sample Size for a Confidence Interval of a Population Proportion     256
Statistical Follies and Fallacies: It Is Plus and Minus the Error Term     258
Hypothesis Testing I: The Six Steps of Statistical Inference      267
Introduction: Scientific Theory and the Development of Testable Hypotheses     267
Making Empirical Predictions     268
Statistical Inference     269
The Importance of Sampling Distributions for Hypothesis Testing     272
The Six Steps of Statistical Inference for a Large Single-Sample Means Test     274
Test Preparation     276
The Six Steps     276
Special Note on Symbols     287
Understanding the Place of Probability Theory in Hypothesis Testing     287
A Focus on p-Values     287
The Level of Significance and Critical Regions of the Sampling Distribution Curve     288
The Level of Confidence     295
Study Hints: Organizing Problem Solutions     295
Solution Boxes Using the Six Steps     297
Interpreting Results When the Null Hypothesis Is Rejected: The Hypothetical Framework of Hypothesis Testing     301
Selecting Which Statistical Test to Use     301
Statistical Follies and Fallacies: Informed Common Sense: Going Beyond Common Sense by Observing Data     302
Hypothesis Testing II: Single-Sample Hypothesis Tests: Establishing the Representativeness of Samples     315
Introduction     315
The Small Single-Sample Means Test      317
The "Students' t" Sampling Distribution     317
Selecting the Critical Probability Score, t[subscript Alpha], from the t-distribution Table     321
Special Note on Symbols     321
What Are Degrees of Freedom?     322
The Six Steps of Statistical Inference for a Small Single-Sample Means Test     324
Gaining a Sense of Proportion About the Dynamics of a Means Test     330
Relationships among Hypothesized Parameters, Observed Sample Statistics, Computed Test Statistics, p-Values, and Alpha Levels     330
Using Single-Sample Hypothesis Tests to Establish Sample Representativeness     340
Target Values for Hypothesis Tests of Sample Representativeness     340
Large Single-Sample Proportions Test     344
The Six Steps of Statistical Inference for a Large Single-Sample Proportions Test     346
What to Do If a Sample Is Found Not to Be Representative?     349
Presentation of Data from Single-Sample Hypothesis Tests     350
A Confidence Interval of the Population Mean When n Is Small     351
Statistical Follies and Fallacies: Issues of Sample Size and Sample Representativeness     353
Bivariate Relationships: t-Test for Comparing the Means of Two Groups     368
Introduction: Bivariate Analysis     368
Difference of Means Tests      369
Joint Occurrences of Attributes     370
Correlation     371
Two-Group Difference of Means Test (t-Test) for Independent Samples     371
The Standard Error and Sampling Distribution for the t-Test of the Difference Between Two Means     374
The Six Steps of Statistical Inference for the Two-Group Difference of Means Test     378
When the Population Variances (or Standard Deviations) Appear Radically Different     380
The Two-Group Difference of Means Test for Nonindependent or Matched-Pair Samples     383
The Six Steps of Statistical Inference for the Two-Group Difference of Means Test for Nonindependent or Matched-Pair Samples     388
Practical versus Statistical Significance     389
The Four Aspects of Statistical Relationships     390
Existence of a Relationship     390
Direction of the Relationship     390
Strength of the Relationship, Predictive Power, and Proportional Reduction in Error     391
Practical Applications of the Relationship     392
When to Apply the Various Aspects of Relationships     393
Relevant Aspects of a Relationship for Two-Group Difference of Means Tests     393
Statistical Follies and Fallacies: Fixating on Differences of Means While Ignoring Differences in Variances      395
Analysis of Variance: Differences Among Means of Three or More Groups     414
Introduction     414
Calculating Main Effects     415
The General Linear Model: Testing the Statistical Significance of Main Effects     418
Determining the Statistical Significance of Main Effects Using ANOVA     421
The F-Ratio Test Statistic     428
How the F-Ratio Turns Out When Group Means Are Not Significantly Different     429
The F-Ratio as a Sampling Distribution     430
Relevant Aspects of a Relationship for ANOVA     432
Existence of the Relationship     432
Direction of the Relationship     432
Strength of the Relationship     433
Practical Applications of the Relationship     434
The Six Steps of Statistical Inference for One-Way ANOVA     437
Tabular Presentation of Results     442
Multivariate Applications of the General Linear Model     442
Similarities Between the t-Test and the F-Ratio Test     443
Statistical Follies and Fallacies: Individualizing Group Findings     444
Nominal Variables: The Chi-Square and Binomial Distributions     464
Introduction: Proportional Thinking About Social Status     464
Crosstab Tables: Comparing the Frequencies of Two Nominal/Ordinal Variables     466
The Chi-Square Test: Focusing on the Frequencies of Joint Occurrences     468
Calculating Expected Frequencies     470
Differences Between Observed and Expected Cell Frequencies     470
Degrees of Freedom for the Chi-Square Test     472
The Chi-Square Sampling Distribution and Its Critical Regions     474
The Six Steps of Statistical Inference for the Chi-Square Test     475
Relevant Aspects of a Relationship for the Chi-Square Test     478
Using Chi-Square as a Difference of Proportions Test     479
Tabular Presentation of Data     481
Small Single-Sample Proportions Test: The Binomial Distribution     483
The Binomial Distribution Equation     484
Shortcut Formula for Expanding the Binomial Equation     486
The Six Steps of Statistical Inference for a Small Single-Sample Proportions Test: The Binomial Distribution Test     489
Statistical Follies and Fallacies: Low Statistical Power When the Sample Size Is Small     492
Bivariate Correlation and Regression: Part 1: Concepts and Calculations     509
Introduction: Improving Best Estimates of a Dependent Variable     509
A Correlation Between Two Interval/Ratio Variables     510
Identifying a Linear Relationship      511
Drawing the Scatterplot     513
Identifying a Linear Pattern     513
Using the Linear Regression Equation to Measure the Effects of X on Y     516
Pearson's r Bivariate Correlation Coefficient     518
Computational Spreadsheet for Calculating Bivariate Correlation and Regression Statistics     519
Characteristics of the Pearson's r Bivariate Correlation Coefficient     521
Understanding the Pearson's r Formulation     522
Regression Statistics     524
The Regression Coefficient or Slope, b     525
The Y-intercept, a     525
Calculating the Terms of the Regression Line Formula     527
For the Especially Inquisitive: The Mathematical Relationship Between Pearson's r Correlation Coefficient and the Regression Coefficient, b     529
Statistical Follies and Fallacies The Failure to Observe a Scatterplot Before Calculating Pearson's r     531
Linear Equations Work Only with a Linear Pattern in the Scatterplot     531
Outlier Coordinates and the Attenuation and Inflation of Correlation Coefficients     532
Bivariate Correlation and Regression: Part 2: Hypothesis Testing and Aspects of a Relationship     552
Introduction: Hypothesis Test and Aspects of a Relationship Between Two Interval/Ratio Variables      552
Organizing Data for the Hypothesis Test     553
The Six Steps of Statistical Inference and the Four Aspects of a Relationship     555
Existence of a Relationship     556
Direction of the Relationship     561
Strength of the Relationship     561
Practical Applications of the Relationship     565
Careful Interpretation of Correlation and Regression Statistics     567
Correlations Apply to a Population, Not to an Individual     567
Careful Interpretation of the Slope, b     568
Distinguishing Statistical Significance from Practical Significance     568
Tabular Presentation: Correlation Tables     570
Statistical Follies and Fallacies: Correlation Does Not Always Indicate Causation     571
Review of Basic Mathematical Operations     586
Statistical Probability Tables     595
Statistical Table A-Random Number Table     595
Statistical Table B-Normal Distribution Table     596
Statistical Table C-t-Distribution Table     598
Statistical Table D-Critical Values of the F-Ratio Distribution at the .05 Level of Significance     599
Statistical Table E-Critical Values of the F-Ratio Distribution at the .01 Level of Significance     600
Statistical Table F-q-Values of Range Tests at the .05 and .01 Levels of Significance     601
Statistical Table G-Critical Values of the Chi-Square Distribution     602
Answers to Selected Chapter Exercises     603
Guide to SPSS for Windows     620
References     649
Index     654