# Introductory Statistics for the Behavioral Sciences

**by**Welkowitz, Joan

### 9780470907764

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## Summary

## Author Biography

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.

## Table of Contents

**Preface xv**

**Acknowledgments xix**

**Glossary of Symbols xxi**

**Part I Descriptive Statistics 1**

**Chapter 1 Introduction 3**

Why Study Statistics? 4

Descriptive and Inferential Statistics 5

Populations, Samples, Parameters, and Statistics 6

Measurement Scales 7

Independent and Dependent Variables 10

Summation Notation 12

Ihno’s Study 16

Summary 18

Exercises 19

Thought Questions 23

Computer Exercises 23

Bridge to SPSS 24

**Chapter 2 Frequency Distributions and Graphs 26**

The Purpose of Descriptive Statistics 27

Regular Frequency Distributions 28

Cumulative Frequency Distributions 30

Grouped Frequency Distributions 31

Real and Apparent Limits 33

Interpreting a Raw Score 34

Definition of Percentile Rank and Percentile 34

Computational Procedures 35

Deciles, Quartiles, and the Median 38

Graphic Representations 39

Shapes of Frequency Distributions 43

Summary 45

Exercises 47

Thought Questions 49

Computer Exercises 49

Bridge to SPSS 50

**Chapter 3 Measures of Central Tendency and Variability 53**

Introduction 54

The Mode 56

The Median 56

The Mean 58

The Concept of Variability 62

The Range 65

The Standard Deviation and Variance 66

Summary 73

Exercises 75

Thought Questions 76

Computer Exercises 77

Bridge to SPSS 78

**Chapter 4 Standardized Scores and the Normal Distribution 81**

Interpreting a Raw Score Revisited 82

Rules for Changing μ and σ 84

Standard Scores (*z* Scores) 85

*T* Scores, SAT Scores, and IQ Scores 88

The Normal Distribution 90

Table of the Standard Normal Distribution 93

Illustrative Examples 95

Summary 101

Exercises 103

Thought Questions 105

Computer Exercises 106

Bridge to SPSS 106

**Part II Basic Inferential Statistics 109**

**Chapter 5 Introduction to Statistical Inference 111**

Introduction 113

The Goals of Inferential Statistics 114

Sampling Distributions 114

The Standard Error of the Mean 119

The *z* Score for Sample Means 122

Null Hypothesis Testing 124

Assumptions Required by the Statistical Test for the Mean of a Single Population 132

Summary 133

Exercises 135

Thought Questions 137

Computer Exercises 138

Bridge to SPSS 138

Appendix: The Null Hypothesis Testing Controversy 139

**Chapter 6 The One-Sample t Test and Interval Estimation 142**

Introduction 143

The Statistical Test for the Mean of a Single Population When σ Is Not Known: The *t* Distributions 144

Interval Estimation 148

The Standard Error of a Proportion 152

Summary 155

Exercises 156

Thought Questions 157

Computer Exercises 158

Bridge to SPSS 158

**Chapter 7 Testing Hypotheses About the Difference Between the Means of Two Populations 160**

The Standard Error of the Difference 162

Estimating the Standard Error of the Difference 166

The *t* Test for Two Sample Means 167

Confidence Intervals for μ1 − μ2 172

The Assumptions Underlying the Proper Use of the *t* Test for Two Sample Means 175

Measuring the Size of an Effect 176

The *t* Test for Matched Samples 178

Summary 185

Exercises 187

Thought Questions 190

Computer Exercises 191

Bridge to SPSS 191

**Chapter 8 Nonparametric Tests for the Difference Between Two Means 194**

Introduction 195

The Difference Between the Locations of Two Independent Samples: The Rank-Sum Test 199

The Difference Between the Locations of Two Matched Samples: The Wilcoxon Test 205

Summary 210

Exercises 212

Thought Questions 215

Computer Exercises 216

Bridge to SPSS 216

**Chapter 9 Linear Correlation 218**

Introduction 219

Describing the Linear Relationship Between Two Variables 222

Interpreting the Magnitude of a Pearson *r* 229

When Is It Important That Pearson’s *r* Be Large? 234

Testing the Significance of the Correlation Coefficient 236

The Relationship Between Two Ranked Variables: The Spearman Rank-Order Correlation Coefficient 239

Summary 242

Exercises 244

Thought Questions 247

Computer Exercises 248

Bridge to SPSS 248

Appendix: Equivalence of the Various Formulas for *r* 251

**Chapter 10 Prediction and Linear Regression 253**

Introduction 254

Using Linear Regression to Make Predictions 254

Measuring Prediction Error: The Standard Error of Estimate 263

The Connection Between Correlation and the *t* Test 265

Estimating the Proportion of Variance Accounted for in the Population 271

Summary 273

Exercises 275

Thought Questions 277

Computer Exercises 277

Bridge to SPSS 278

**Chapter 11 Introduction to Power Analysis 281**

Introduction 282

Concepts of Power Analysis 283

The Significance Test of the Mean of a Single Population 285

The Significance Test of the Proportion of a Single Population 290

The Significance Test of a Pearson *r* 292

Testing the Difference Between Independent Means 293

Testing the Difference Between the Means of Two Matched Populations 297

Choosing a Value for **d** for a Power Analysis Involving Independent Means 299

Using Power Analysis Concepts to Interpret the Results of Null Hypothesis Tests 301

Summary 304

Exercises 306

Thought Questions 308

Computer Exercises 309

Bridge to SPSS 310

**Part III Analysis of Variance Methods 313**

**Chapter 12 One-Way Analysis of Variance 315**

Introduction 317

The General Logic of ANOVA 318

Computational Procedures 321

Testing the *F* Ratio for Statistical Significance 326

Calculating the One-Way ANOVA From Means and Standard Deviations 328

Comparing the One-Way ANOVA With the *t* Test 329

A Simplified ANOVA Formula for Equal Sample Sizes 330

Effect Size for the One-Way ANOVA 331

Some Comments on the Use of ANOVA 333

A Nonparametric Alternative to the One-Way ANOVA: The Kruskal-Wallis *H* Test 336

Summary 339

Exercises 343

Thought Questions 346

Computer Exercises 346

Bridge to SPSS 346

Appendix: Proof That the Total Sum of Squares Is Equal to the Sum of the Between-Group and the Within-Group Sum of Squares 348

**Chapter 13 Multiple Comparisons 349**

Introduction 350

Fisher’s Protected *t* Tests and the Least Significant Difference (LSD) 351

Tukey’s Honestly Significant Difference (HSD) 355

Other Multiple Comparison Procedures 360

Planned and Complex Comparisons 362

Nonparametric Multiple Comparisons: The Protected Rank-Sum Test 365

Summary 366

Exercises 368

Thought Questions 369

Computer Exercises 370

Bridge to SPSS 370

**Chapter 14 Introduction to Factorial Design: Two-Way Analysis of Variance 372**

Introduction 373

Computational Procedures 374

The Meaning of Interaction 384

Following Up a Significant Interaction 387

Measuring Effect Size in a Factorial ANOVA 390

Summary 392

Exercises 395

Thought Questions 398

Computer Exercises 399

Bridge to SPSS 399

**Chapter 15 Repeated-Measures ANOVA 402**

Introduction 403

Calculating the One-Way RM ANOVA 403

Rationale for the RM ANOVA Error Term 408

Assumptions and Other Considerations Involving the RM ANOVA 408

The RM Versus RB Design: An Introduction to the Issues of Experimental Design 411

The Two-Way Mixed Design 415

Summary 423

Exercises 428

Thought Questions 430

Computer Exercises 430

Bridge to SPSS 431

**Part IV Nonparametric Statistics for Categorical Data 435**

**Chapter 16 Probability of Discrete Events and the Binomial Distribution 437**

Introduction 438

Probability 439

The Binomial Distribution 442

The Sign Test for Matched Samples 448

Summary 450

Exercises 451

Thought Questions 453

Computer Exercises 453

Bridge to SPSS 454

**Chapter 17 Chi-Square Tests 457**

Chi Square and the Goodness of Fit: One-Variable Problems 458

Chi Square as a Test of Independence: Two-Variable Problems 464

Measures of Strength of Association in Two-Variable Tables 470

Summary 472

Exercises 474

Thought Questions 476

Computer Exercises 477

Bridge to SPSS 478

**Appendix 481**

Statistical Tables 483

Answers to Odd-Numbered Exercises 499

Data From Ihno’s Experiment 511

**Glossary of Terms 515**

**References 525**

**Index 527**