Introductory Statistics for the Behavioral Sciences

JOAN WELKOWITZ, PhD, (deceased) was professor of psychology at New York University. She directed the graduate clinical program for ten years. She taught courses in methodology and statistics at both the graduate and undergraduate levels for more than twenty-five years and?was the primary author of Introductory Statistics for the Behavioral Sciences.BARRY H. COHEN, PhD, is the Director of the master's program in psychology at New York University, where he has been teaching statistics for more than twenty years. He is the coauthor of two other successful statistics books from Wiley—Explaining Psychological Statistics, Third Edition, and Essentials of Statistics for the Social and Behavioral Sciences.R. BROOKE LEA, PhD, is professor and chair of the Psychology Department at Macalester College, St. Paul, Minnesota.?His research publications concern the comprehension processes that occur during reading of text and poetry.

• Preface xv Acknowledgments xixGlossary of Symbols xxiPart I Descriptive Statistics 1Chapter 1 Introduction 3Why Study Statistics? 4Descriptive and Inferential Statistics 5Populations, Samples, Parameters, and Statistics 6Measurement Scales 7Independent and Dependent Variables 10Summation Notation 12Ihno’s Study 16Summary 18Exercises 19Thought Questions 23Computer Exercises 23Bridge to SPSS 24Chapter 2 Frequency Distributions and Graphs 26The Purpose of Descriptive Statistics 27Regular Frequency Distributions 28Cumulative Frequency Distributions 30Grouped Frequency Distributions 31Real and Apparent Limits 33Interpreting a Raw Score 34Definition of Percentile Rank and Percentile 34Computational Procedures 35Deciles, Quartiles, and the Median 38Graphic Representations 39Shapes of Frequency Distributions 43Summary 45Exercises 47Thought Questions 49Computer Exercises 49Bridge to SPSS 50Chapter 3 Measures of Central Tendency and Variability 53Introduction 54The Mode 56The Median 56The Mean 58The Concept of Variability 62The Range 65The Standard Deviation and Variance 66Summary 73Exercises 75Thought Questions 76Computer Exercises 77Bridge to SPSS 78Chapter 4 Standardized Scores and the Normal Distribution 81Interpreting a Raw Score Revisited 82Rules for Changing μ and σ 84Standard Scores (z Scores) 85T Scores, SAT Scores, and IQ Scores 88The Normal Distribution 90Table of the Standard Normal Distribution 93Illustrative Examples 95Summary 101Exercises 103Thought Questions 105Computer Exercises 106Bridge to SPSS 106Part II Basic Inferential Statistics 109Chapter 5 Introduction to Statistical Inference 111Introduction 113The Goals of Inferential Statistics 114Sampling Distributions 114The Standard Error of the Mean 119The z Score for Sample Means 122Null Hypothesis Testing 124Assumptions Required by the Statistical Test for the Mean of a Single Population 132Summary 133Exercises 135Thought Questions 137Computer Exercises 138Bridge to SPSS 138Appendix: The Null Hypothesis Testing Controversy 139Chapter 6 The One-Sample t Test and Interval Estimation 142Introduction 143The Statistical Test for the Mean of a Single Population When σ Is Not Known: The t Distributions 144Interval Estimation 148The Standard Error of a Proportion 152Summary 155Exercises 156Thought Questions 157Computer Exercises 158Bridge to SPSS 158Chapter 7 Testing Hypotheses About the Difference Between the Means of Two Populations 160The Standard Error of the Difference 162Estimating the Standard Error of the Difference 166The t Test for Two Sample Means 167Confidence Intervals for μ1 − μ2 172The Assumptions Underlying the Proper Use of the t Test for Two Sample Means 175Measuring the Size of an Effect 176The t Test for Matched Samples 178Summary 185Exercises 187Thought Questions 190Computer Exercises 191Bridge to SPSS 191Chapter 8 Nonparametric Tests for the Difference Between Two Means 194Introduction 195The Difference Between the Locations of Two Independent Samples: The Rank-Sum Test 199The Difference Between the Locations of Two Matched Samples: The Wilcoxon Test 205Summary 210Exercises 212Thought Questions 215Computer Exercises 216Bridge to SPSS 216Chapter 9 Linear Correlation 218Introduction 219Describing the Linear Relationship Between Two Variables 222Interpreting the Magnitude of a Pearson r 229When Is It Important That Pearson’s r Be Large? 234Testing the Significance of the Correlation Coefficient 236The Relationship Between Two Ranked Variables: The Spearman Rank-Order Correlation Coefficient 239Summary 242Exercises 244Thought Questions 247Computer Exercises 248Bridge to SPSS 248Appendix: Equivalence of the Various Formulas for r 251Chapter 10 Prediction and Linear Regression 253Introduction 254Using Linear Regression to Make Predictions 254Measuring Prediction Error: The Standard Error of Estimate 263The Connection Between Correlation and the t Test 265Estimating the Proportion of Variance Accounted for in the Population 271Summary 273Exercises 275Thought Questions 277Computer Exercises 277Bridge to SPSS 278Chapter 11 Introduction to Power Analysis 281Introduction 282Concepts of Power Analysis 283The Significance Test of the Mean of a Single Population 285The Significance Test of the Proportion of a Single Population 290The Significance Test of a Pearson r 292Testing the Difference Between Independent Means 293Testing the Difference Between the Means of Two Matched Populations 297Choosing a Value for d for a Power Analysis Involving Independent Means 299Using Power Analysis Concepts to Interpret the Results of Null Hypothesis Tests 301Summary 304Exercises 306Thought Questions 308Computer Exercises 309Bridge to SPSS 310Part III Analysis of Variance Methods 313Chapter 12 One-Way Analysis of Variance 315Introduction 317The General Logic of ANOVA 318Computational Procedures 321Testing the F Ratio for Statistical Significance 326Calculating the One-Way ANOVA From Means and Standard Deviations 328Comparing the One-Way ANOVA With the t Test 329A Simplified ANOVA Formula for Equal Sample Sizes 330Effect Size for the One-Way ANOVA 331Some Comments on the Use of ANOVA 333A Nonparametric Alternative to the One-Way ANOVA: The Kruskal-Wallis H Test 336Summary 339Exercises 343Thought Questions 346Computer Exercises 346Bridge to SPSS 346Appendix: Proof That the Total Sum of Squares Is Equal to the Sum of the Between-Group and the Within-Group Sum of Squares 348Chapter 13 Multiple Comparisons 349Introduction 350Fisher’s Protected t Tests and the Least Significant Difference (LSD) 351Tukey’s Honestly Significant Difference (HSD) 355Other Multiple Comparison Procedures 360Planned and Complex Comparisons 362Nonparametric Multiple Comparisons: The Protected Rank-Sum Test 365Summary 366Exercises 368Thought Questions 369Computer Exercises 370Bridge to SPSS 370Chapter 14 Introduction to Factorial Design: Two-Way Analysis of Variance 372Introduction 373Computational Procedures 374The Meaning of Interaction 384Following Up a Significant Interaction 387Measuring Effect Size in a Factorial ANOVA 390Summary 392Exercises 395Thought Questions 398Computer Exercises 399Bridge to SPSS 399Chapter 15 Repeated-Measures ANOVA 402Introduction 403Calculating the One-Way RM ANOVA 403Rationale for the RM ANOVA Error Term 408Assumptions and Other Considerations Involving the RM ANOVA 408The RM Versus RB Design: An Introduction to the Issues of Experimental Design 411The Two-Way Mixed Design 415Summary 423Exercises 428Thought Questions 430Computer Exercises 430Bridge to SPSS 431Part IV Nonparametric Statistics for Categorical Data 435Chapter 16 Probability of Discrete Events and the Binomial Distribution 437Introduction 438Probability 439The Binomial Distribution 442The Sign Test for Matched Samples 448Summary 450Exercises 451Thought Questions 453Computer Exercises 453Bridge to SPSS 454Chapter 17 Chi-Square Tests 457Chi Square and the Goodness of Fit: One-Variable Problems 458Chi Square as a Test of Independence: Two-Variable Problems 464Measures of Strength of Association in Two-Variable Tables 470Summary 472Exercises 474Thought Questions 476Computer Exercises 477Bridge to SPSS 478Appendix 481Statistical Tables 483Answers to Odd-Numbered Exercises 499Data From Ihno’s Experiment 511Glossary of Terms 515References 525Index 527