Introductory Statistics for the Behavioral Sciences

R. BROOKE LEA, PhD, is DeWitt Wallace Professor of Psychology and Director of Cognitive Science at Macalester College in Saint Paul, MN, where he has taught psychological statistics for more than 25 years. He is a cognitive psychologist who studies reasoning and language processing, with a special interest in the role that poetic devices—such as rhyme, alliteration, and meter—play in the comprehension of poetry. BARRY H. COHEN, Ph.D. earned a B.S. in Physics and a Ph.D in experimental psychology. Until his retirement, he was the director of the MA program in psychology at NYU, and taught statistics and research design at the graduate level there for more than 30 years. He is now spending his active retirement by collaborating on meditation research.

• Preface xiAcknowledgments xvGlossary of Symbols xviiPart I Descriptive Statistics 1Chapter 1 Introduction 3Why Study Statistics? 4Descriptive and Inferential Statistics 5Populations, Samples, Parameters, and Statistics 5Measurement Scales 6Independent and Dependent Variables 8Summation Notation 10Jackson’s Study 14Summary 15Exercises 16Thought Questions 19Computer Exercises 19Bridge to SPSS 20Chapter 2 Frequency Distributions and Graphs 22Purpose of Descriptive Statistics 23Regular Frequency Distributions 23Cumulative Frequency Distributions 25Grouped Frequency Distributions 27Real and Apparent Limits 28Graphic Representations 29Skewing of Frequency Distributions 32Summary 34Exercises 35Thought Questions 36Computer Exercises 37Bridge to SPSS 37Chapter 3 Measures of Central Tendency and Variability 40Introduction 41The Mode 42The Median 43The Mean 44The Concept of Variability 47The Range 49The Standard Deviation and Variance 50Summary 55Exercises 57Thought Questions 58Computer Exercises 58Bridge to SPSS 59Chapter 4 Standardized Scores and the Normal Distribution 61Interpreting a Raw Score Revisited 62Rules for Changing μ and σ 63Standard Scores (z-Scores) 64T Scores, SAT Scores, and IQ Scores 67The Normal Distribution 68Table of the Standard Normal Distribution 70Illustrative Examples 71Summary 77Exercises 78Thought Questions 80Computer Exercises 80Bridge to SPSS 81Part II Basic Inferential Statistics 83Chapter 5 Introduction to Statistical Inference 85Introduction 86The Goals of Inferential Statistics 87Sampling Distributions 87The Standard Error of the Mean 93The z-Score for Sample Means 95Null Hypothesis Testing 96Assumptions Required by the Statistical Test for the Mean of a Single Population 103Why is Null Hypothesis Testing So Misunderstood? 104Summary 105Exercises 107Thought Questions 108Computer Exercises 108Bridge to SPSS 109Chapter 6 One-Sample t Test and Interval Estimation 110Introduction 110Statistical Test for the Mean of a Single Population When σ Is Not Known: The t Distributions 111Interval Estimation 115Computation 116Working with Proportions 118Summary 121Exercises 122Thought Questions 123Computer Exercises 123Bridge to SPSS 124Chapter 7 Testing Hypotheses About the Difference Between the Means of Two Populations 126The Standard Error of the Difference 127Estimating the Standard Error of the Difference 130The t Test for Two Independent Sample Means 131Confidence Intervals for μ 1 − μ 2 135Measuring the Size of an Effect for a Difference Between Two Independent Samples 136Reporting the Results of a t Test with a CI and a Measure of Effect Size 137The Assumptions Underlying the Proper Use of the t Test for Two Sample Means 138The t Test for Matched Samples 140Summary 146Exercises 148Thought Questions 150Computer Exercises 151Bridge to SPSS 151Chapter 8 Nonparametric Tests for the Difference Between Two Means 155Introduction 156The Difference Between the Locations of Two Independent Samples: The Rank-Sum Test 159The Difference Between the Locations of Two Matched Samples: The Wilcoxon Test 163Summary 167Exercises 169Thought Questions 172Computer Exercises 172Bridge to SPSS 172Chapter 9 Linear Correlation 175Introduction 176Describing the Linear Relationship Between Two Variables 178Interpreting the Magnitude of a Pearson r 184When Is It Important That Pearson’s r Be Large? 190Testing the Significance of the Correlation Coefficient 191The Relationship Between Two Ranked Variables: The Spearman Rank-Order Correlation Coefficient 192Summary 195Exercises 196Thought Questions 199Computer Exercises 200Bridge to SPSS 200Appendix: Equivalence of the Various Formulas for r 203Chapter 10 Prediction and Linear Regression 205Introduction 206Using Linear Regression to Make Predictions 206Measuring Prediction Error: The Standard Error of Estimate 212The Connection Between Correlation and the t Test 214Estimating the Proportion of Variance Accounted for in the Population 219Summary 220Exercises 222Thought Questions 224Computer Exercises 224Bridge to SPSS 225Chapter 11 Introduction to Power Analysis 228Introduction 229Concepts of Power Analysis 230Power Analysis for the Mean of a Single Population 231Power Analysis for the Proportion of a Single Population 235Power Analysis for a Pearson r 236Power Analysis for the Difference Between Independent Means 237Power Analysis for the Difference Between the Means of Two Matched Populations 241Choosing a Value for d for a Power Analysis Involving Independent Means 242Using Power Analysis Concepts to Interpret the Results of Null Hypothesis Tests 243The Null Hypothesis Testing Controversy Revisited 244Summary 245Exercises 248Thought Questions 250Computer Exercises 250Bridge to SPSS 251Chapter 12 Beyond Traditional Null Hypothesis Testing 254More on Criticisms of NHT (and Some Rebuttals) 254Improving NHT with Robust Statistics 257p Hacking, HARKing, and the “File Drawer Problem” 260The Replication Crisis in Psychological Research and Possible Solutions 262Alternatives to NHT (The “New” Statistics) 264Summary 266Thought Questions 267Appendix: A Brief Introduction to the Use of Bayesian Statistics 268Part III Analysis of Variance Methods 271Chapter 13 One-Way Analysis of Variance 273Introduction 274The General Logic of ANOVA 275Computational Procedures 278Testing the F Ratio for Statistical Significance 281Calculating the One-Way ANOVA From Means and Standard Deviations 282Comparing the One-Way ANOVA With the t Test 284A Simplified ANOVA Formula for Equal Sample Sizes 284Effect Size for the One-Way ANOVA 285Some Comments on the Use of ANOVA 287A Nonparametric Alternative to the One-Way ANOVA: The Kruskal–Wallis H Test 289Summary 291Exercises 294Thought Questions 297Computer Exercises 297Bridge to SPSS 297Appendix: Proof That the Total Sum of Squares Is Equal to the Sum of the Between-Group and the Within-Group Sum of Squares 301Chapter 14 Multiple Comparisons 302Introduction 303Fisher’s Protected t Tests and the Least Significant Difference (LSD) 303Tukey’s Honestly Significant Difference (HSD) 307Other Multiple Comparison Procedures 310Planned and Complex Comparisons 311Nonparametric Multiple Comparisons: The Protected Rank-Sum Test 313Summary 314Exercises 315Thought Questions 316Computer Exercises 316Bridge to SPSS 317Chapter 15 Introduction to Factorial Design: Two-Way Analysis of Variance 319Introduction 320Computational Procedures 321The Meaning of Interaction 328Following Up on a Significant Interaction 330Measuring Effect Size in a Factorial ANOVA 332Summary 333Exercises 337Thought Questions 339Computer Exercises 339Bridge to SPSS 340Chapter 16 Repeated-Measures ANOVA 344Introduction 345Calculating the One-Way RM ANOVA 345Rationale for the RM ANOVA Error Term 348Assumptions and Other Considerations Involving the RM ANOVA 349The RM Versus RB Design: An Introduction to the Issues of Experimental Design 351The Two-Way Mixed Design 354Summary 359Exercises 363Thought Questions 365Computer Exercises 365Bridge to SPSS 365Part IV Nonparametric Statistics for Categorical Data 371Chapter 17 Probability of Discrete Events and the Binomial Distribution 373Introduction 373Probability 374The Binomial Distribution 377The Sign Test for Matched Samples 381Summary 382Exercises 383Exercises 385Computer Exercises 385Bridge to SPSS 385Chapter 18 Chi-Square Tests 389Introduction 389Chi-Square and the Goodness of Fit: One-Variable Problems 390Chi-Square as a Test of Independence: Two-Variable Problems 394Measures of Strength of Association in Two-Variable Tables 399Summary 401Exercises 402Thought Questions 404Computer Exercises 404Bridge to SPSS 405Appendix 409Statistical Tables 411Answer Key 426Data from Jackson’s Experiment 434Glossary of Terms 435References 444Index 000