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1 INTRODUCTION: STATISTICS AND DATA ANALYSIS AS TOOLS FOR RESEARCHERS3

2 PROCESS OF RESEARCH IN PSYCHOLOGY AND RELATED FIELDS45

3 FREQUENCY DISTRIBUTIONS, GRAPHING, AND DATA DISPLAY85

4 DESCRIPTIVE STATISTICS: CENTRAL TENDENCY AND VARIABILITY133

5 STANDARD SCORES AND THE NORMAL DISTRIBUTION177

6 CORRELATION205

7 LINEAR REGRESSION241

8 PROBABILITY273

9 INFERENTIAL STATISTICS: SAMPLING DISTRIBUTIONS AND HYPOTHESIS TESTING315

10 MEAN COMPARISON Ⅰ: THE t TEST365

11 MEAN COMPARISON Ⅱ: ONE-VARIABLE ANALYSIS OF VARIANCE411

12 MEAN COMPARISON Ⅲ: TWO-VARIABLE ANALYSIS OF VARIANCE459

13 MEAN COMPARISON Ⅳ: ONE-VARIABLE REPEATED-MEASURES ANALYSIS OF VARIANCE499

14 SOME NONPARAMETRIC STATISTICS FOR CATEGORICAL AND ORDINAL DATA523

15 CONCLUSION: STATISTICS AND DATA ANALYSIS IN CONTEXT563

1 INTRODUCTION: STATISTICS AND DATA ANALYSIS AS TOOLS FOR RESEARCHERS3

DATA BOX 1.A: What Is or Are Data?5

Tools for Inference: David L.'s Problem5

College Choice6

College Choice: What Would (Did) You Do?6

Statistics Is the Science of Data, Not Mathematics8

Statistics, Data Analysis, and the Scientific Method9

Inductive and Deductive Reasoning10

Populations and Samples12

Descriptive and Inferential Statistics16

DATA BOX 1.B: Reactions to the David L. Problem18

Knowledge Base19

Discontinuous and Continuous Variables20

DATA BOX 1.c: Rounding and Continuous Variables22

Writing About Data: Overview and Agenda23

Scales of Measurement24

Nominal Scales25

Ordinal Scales26

Interval Scales27

Ratio Scales28

Writing About Scales29

Knowledge Base31

Overview of Statistical Notation31

What to Do When: Mathematical Rules of Priority34

DATA BOX 1.D: The Size of Numbers is Relative38

Mise en Place39

About Calculators39

Knowledge Base40

PROJECT EXERCISE: Avoiding Statisticophobia40

Looking Forward, Then Back41

Summary42

Key Terms42

Problems42

2 PROCESS OF RESEARCH IN PSYCHOLOGY AND RELATED FIELDS45

The Research Loop of Experimentation: An Overview of the Research Process45

Populations and Samples Revisited: The Role of Randomness48

Distinguishing Random Assignment from Random Sampling48

Some Other Randomizing Procedures50

Sampling Error52

Knowledge Base53

DATA BOX 2.A: Recognizing Randomness, Imposing Order54

Independent and Dependent Variables54

Types of Dependent Measures58

Closing or Continuing the Research Loop?60

DATA BOX 2.B: Variable Distinctions: Simple, Sublime, and All Too Easily Forgotten61

The Importance of Determining Causality61

DATA BOX 2.C: The “Hot Hand in Basketball” and the Misrepresentation of Randomness62

Operational Definitions in Behavioral Research63

Writing Operational Definitions64

Knowledge Base64

Reliability and Validity65

Reliability66

Validity67

Knowledge Base69

Research Designs70

Correlational Research70

Experiments72

Quasi-experiments74

DATA BOX 2.D: Quasi-experimentation in Action: What to Do Without Random Assignment or a Control Group75

Knowledge Base76

PROJECT EXERCISE: Using a Random Numbers Table77

Looking Forward, Then Back81

Summary81

Key Terms82

Problems82

3 FREQUENCY DISTRIBUTIONS, GRAPHING, AND DATA DISPLAY85

What is a Frequency Distribution?87

DATA BOX 3.A: Dispositional Optimism and Health: A Lot About the LOT88

Proportions and Percentages90

Grouping Frequency Distributions92

True Limits and Frequency Distributions95

Knowledge Base96

Graphing Frequency Distributions97

Bar Graphs98

Histograms99

Frequency Polygons100

Misrepresenting Relationships: Biased or Misleading Graphs102

New Alternatives for Graphing Data: Exploratory Data Analysis104

Stem and Leaf Diagrams105

DATA BOX 3.B: Biased Graphical Display—Appearances Can Be Deceiving106

Tukey's Tallies108

Knowledge Base109

Envisioning the Shape of Distributions111

DATA BOX 3.c: Kurtosis, or What's the Point Spread?113

DATA BOX 3.D: Elegant Information—Napoleon's Ill-fated March to Moscow114

Percentiles and Percentile Ranks115

Cumulative Frequency116

Cumulative Percentage117

Calculating Percentile Rank118

Reversing the Process: Finding Scores from Percentile Ranks119

Exploring Data: Calculating the Middle Percentiles and Quartiles120

Writing About Percentiles122

Knowledge Base123

Constructing Tables and Graphs123

Less is More: Avoiding Chartjunk and Tableclutter, and Other Suggestions124

American Psychological Association (APA) Style Guidelines for Data Display125

PROJECT EXERCISE: Discussing the Benefits of Accurate but Persuasive Data Display126

Looking Forward, Then Back127

Summary128

Key Terms129

Problems129

4 DESCRIPTIVE STATISTICS: CENTRAL TENDENCY AND VARIABILITY133

Why Represent Data By Central Tendency134

The Mean: The Behavioral Scientist's Statistic of Choice136

DATA BOX 4.A: How Many Are There? And Where Did They Come138

From? Proper Use of N and n138

Calculating Means from Ungrouped and Grouped Data138

Caveat Emptor: Sensitivity to Extreme Scores140

Weighted Means: An Approach for Determining Averages of Different-Sized Groups142

DATA BOX 4.B: Self-Judgment Under Uncertainty—Being Average is Sometimes OK143

The Median144

The Mode145

The Utility of Central Tendency147

Shapes of Distributions and Central Tendency147

When to Use Which Measure of Central Tendency148

Writing About Central Tendency149

Knowledge Base150

Understanding Variability151

The Range153

The Interquartile and the Semi-Interquartile Range153

Variance and Standard Deviation155

Sample Variance and Standard Deviation157

Homogeneity and Heterogeneity: Understanding the Standard Deviations of Different Distributions159

Calculating Variance and Standard Deviation from a Data Array160

Population Variance and Standard Deviation161

Looking Ahead: Biased and Unbiased Estimators of Variance and Standard Deviation162

DATA BOX 4.c: Avoid Computation Frustration: Get to Know Your Calculator165

Knowledge Base165

Factors Affecting Variability166

Writing About Range, Variance, and Standard Deviation168

DATA BOX 4.D: Sample Size and Variability—The Hospital Problem169

PROJECT EXERCISE: Proving the Least Squares Principle for the Mean170

Looking Forward, Then Back171

Summary172

Key Terms173

Problems173

5 STANDARD SCORES AND THE NORMAL DISTRIBUTION177

DATA BOX 5.A: Social Comparison Among Behavioral and Natural Scientists: How Many Peers Review Research Before Publication?179

DATA BOX 5.B: Explaining the Decline in SAT Scores: Lay Versus Statistical Accounts180

Why Standardize Measures?181

The z Score: A Conceptual Introduction182

Formulas for Calculating z Scores185

The Standard Normal Distribution186

Standard Deviation Revisited: The Area Under the Normal Curve187

Application: Comparing Performance on More than One Measure188

Knowledge Base189

Working with z Scores and the Normal Distribution190

Finding Percentile Ranks with z Scores191

Further Examples of Using z Scores to Identify Areas Under the Normal Curve192

DATA BOX 5.C: Intelligence, Standardized IQ Scores, and the Normal Distribution194

A Further Transformed Score: The T Score196

Writing About Standard Scores and the Normal Distribution197

Knowledge Base198

Looking Ahead: Probability, z Scores, and the Normal Distribution198

PROJECT EXERCISE: Understanding the Recentering of Scholastic Aptitude Test Scores199

Looking Forward, Then Back201

Summary202

Key Terms202

Problems202

6 CORRELATION205

Association, Causation, and Measurement206

Galton, Pearson, and the Index of Correlation207

A Brief But Essential Aside: Correlation Does Not Imply Causation207

The Pearson Correlation Coefficient209

Conceptual Definition of the Pearson r209

DATA BOX 6.A: Mood as Misbegotten: Correlating Predictors with Mood States213

Calculating the Pearson r216

Interpreting Correlation221

Magnitude of r222

Coefficients of Determination and Nondetermination222

Factors Influencing r224

Writing About Correlational Relationships226

Knowledge Base227

Correlation as Consistency and Reliability228

DATA BOX 6.B: Personality, Cross-Situational Consistency, and Correlation228

Other Types of Reliability Defined229

A Brief Word About Validity229

DATA BOX 6.c: Examining a Correlation Matrix: A Start for Research230

What to Do When: A Brief, Conceptual Guide to Other Measures of Association231

DATA BOX 6.D: Perceived Importance of Scientific Topics and Evaluation Bias232

PROJECT EXERCISE: Identifying Predictors of Your Mood233

Looking Forward, Then Back237

Summary237

Key Terms238

Problems238

7 LINEAR REGRESSION241

Simple Linear Regression242

The z Score Approach to Regression242

Computational Approaches to Regression243

The Method of Least Squares for Regression245

Knowledge Base249

DATA BOX 7.A: Predicting Academic Success250

Residual Variation and the Standard Error of Estimate251

DATA BOX 7.B: The Clinical and the Statistical: Intuition Versus Prediction253

Assumptions Underlying the Standard Error of Estimate253

Partitioning Variance: Explained and Unexplained Variation256

A Reprise for the Coefficients of Determination and Nondetermination257

Proper Use of Regression: A Brief Recap258

Knowledge Base258

Regression to the Mean259

DATA BOX 7.c: Reinforcement, Punishment, or Regression Toward the Mean?260

Regression as a Research Tool261

Other Applications of Regression in the Behavioral Sciences262

Writing About Regression Results263

Multivariate Regression: A Conceptual Overview263

PROJECT EXERCISE: Perceiving Risk and Judging the Frequency of Deaths264

Looking Forward, Then Back268

Summary268

Key Terms269

Problems269

8 PROBABILITY273

The Gambler's Fallacy or Randomness Revisited275

Probability: A Theory of Outcomes277

Classical Probability Theory277

DATA BOX B.A: “I Once Knew a Man Who&”: Beware Man-Who Statistics278

Probability's Relationship to Proportion and Percentage281

DATA BOX 8.B: Classical Probability and Classic Probability Examples282

Probabilities Can Be Obtained from Frequency Distributions283

Knowledge Base283

DATA BOX 8.c: A Short History of Probability284

Calculating Probabilities Using the Rules for Probability285

The Addition Rule for Mutually Exclusive and Nonmutually Exclusive Events285

The Multiplication Rule for Independent and Conditional Probabilities287

DATA BOX 8.D: Conjunction Fallacies: Is Linda a Bank Teller or a Feminist Bank Teller?288

Multiplication Rule for Dependent Events293

Knowledge Base293

Using Probabilities with the Standard Normal Distribution: z Scores Revisited294

Determining Probabilities with the Binomial Distribution: An Overview299

Working with the Binomial Distribution300

Approximating the Standard Normal Distribution with the Binomial Distribution301

DATA BOX 8.E: Control, Probability, and When the Stakes Are High304

Knowledge Base305

p Values: A Brief Introduction305

Writing About Probability306

PROJECT EXERCISE: Flipping Coins and the Binomial Distribution307

Looking Forward, Then Back310

Summary310

Key Terms311

Problems311

9 INFERENTIAL STATISTICS: SAMPLING DISTRIBUTIONS AND HYPOTHESIS TESTING315

Samples, Population, and Hypotheses: Links to Estimation and Experimentation316

Point Estimation317

Statistical Inference and Hypothesis Testing318

The Distribution of Sample Means319

Expected Value and Standard Error320

The Central Limit Theorem322

Law of Large Numbers Redux322

DATA BOX 9.A: The Law of Small Numbers Revisited323

Standard Error and Sampling Error in Depth324

Estimating the Standard Error of the Mean324

Standard Error of the Mean: A Concrete Example Using Population Parameters326

Defining Confidence Intervals Using the Standard Error of the Mean327

DATA BOX 9.B: Standard Error as an Index of Stability and Reliability of Means328

Knowledge Base329

DATA BOX 9.C: Representing Standard Error Graphically330

Asking and Testing Focused Questions: Conceptual Rationale for Hypotheses331

DATA BOX 9.D: What Constitutes a Good Hypothesis?332

Directional and Nondirectional Hypotheses333

The Null and the Experimental Hypothesis333

Statistical Significance: A Concrete Account336

DATA BOX 9.E: Distinguishing Between Statistical and Practical Significance337

Critical Values: Establishing Criteria for Rejecting the Null Hypothesis338

One- and Two-Tailed Tests340

Degrees of Freedom341

DATA BOX 9.F: When the Null Hypothesis is Rejected—Evaluating Results with the MAGIC Criteria342

Knowledge Base343

Single Sample Hypothesis Testing: The z Test and the Significance of r343

What Is the Probability a Sample Is from One Population or Another?344

Is One Sample Different from a Known Population?345

When Is a Correlation Significant?347

Inferential Errors Types Ⅰ and Ⅱ349

Statistical Power and Effect Size351

Effect Size354

Writing About Hypotheses and the Results of Statistical Tests355

Knowledge Base357

PROJECT EXERCISE: Thinking About Statistical Significance in the Behavioral Science Literature357

Looking Forward, Then Back360

Summary360

Key Terms362

Problems362

10 MEAN COMPARISON I: THE t TEST365

Recapitulation: Why Compare Means?367

The Relationship Between the t and the z Distributions368

The t Distribution368

Assumptions Underlying the t Test369

DATA BOX 10.A: Some Statistical History: Who was “A Student”?371

Hypothesis Testing with t: One-Sample Case372

Confidence Intervals for the One-Sample t Test375

DATA BOX 10.B: The Absolute Value of t376

Power Issues and the One-Sample t Test377

Knowledge Base377

Hypothesis Testing with Two Independent Samples378

Standard Error Revised: Estimating the Standard Error of the Difference Between Means379

Comparing Means: A Conceptual Model and an Aside for Future Statistical Tests383

The t Test for Independent Groups384

DATA BOX 10.C: Language and Reporting Results, or (Too) Great Expectations388

Effect Size and the t Test388

Characterizing the Degree of Association Between the Independent Variable and the Dependent Measure389

DATA BOX 10.D: Small Effects Can Be Impressive Too390

Knowledge Base392

Hypothesis Testing with Correlated Research Designs393

The Statistical Advantage of Correlated Groups Designs: Reducing Error Variance395

The t Test for Correlated Groups396

Calculating Effect Size for Correlated Research Designs399

A Brief Overview of Power Analysis: Thinking More Critically About Research and Data Analysis400

Knowledge Base402

PROJECT EXERCISE: Planning for Data Analysis: Developing a Before and After Data Collection Analysis Plan402

Looking Forward, Then Back405

Summary405

Key Terms406

Problems406

11 MEAN COMPARISON Ⅱ: ONE-VARIABLE ANALYSIS OF VARIANCE411

Overview of the Analysis of Variance413

Describing the F Distribution417

Comparing the ANOVA to the t Test: Shared Characteristics and Assumptions418

Problematic Probabilities: Multiple t Tests and the Risk of Type I Error420

DATA BOX 11.A: R. A. Fischer: Statistical Genius and Vituperative Visionary422

How is the ANOVA Distinct from Prior Statistical Tests? Some Advantages423

Omnibus Test: Comparing More than Two Means Simultaneously423

DATA BOX 1 1.B: Linguistically Between a Rock and Among Hard Places424

Experimentwise Error: Protecting Against Type I Error424

Causality and Complexity425

Knowledge Base426

One-Factor Analysis of Variance426

Identifying Statistical Hypotheses for the ANOVA427

Some Notes on Notation and the ANOVA's Steps429

DATA BOX 1 1.C: Yet Another Point of View on Variance: The General Linear Model431

One-Way ANOVA from Start to Finish: An Example with Data431

Post Hoc Comparisons of Means: Exploring Relations in the “Big, Dumb F”439

Tukey's Honestly Significant Difference Test440

Effect Size for the F Ratio442

Estimating the Degree of Association Between the Independent Variable and the Dependent Measure443

DATA BOX 11.D: A Variance Paradox—Explaining Variance Due to Skill or Baseball is Life444

Writing About the Results of a One-Way ANOVA445

Knowledge Base446

An Alternative Strategy for Comparing Means: A Brief Introduction to Contrast Analysis447

PROJECT EXERCISE: Writing and Exchanging Letters About the ANOVA451

Looking Forward, Then Back452

Summary453

Key Terms454

Problems454

12 MEAN COMPARISON Ⅲ: TWO-VARIABLE ANALYSIS OF VARIANCE459

Overview of Complex Research Designs: Life Beyond Manipulating One Variable460

Two-Factor Analysis of Variance461

DATA BOX 12.A: Thinking Factorially463

Reading Main Effects and the Concept of Interaction465

Statistical Assumptions of the Two-Factor ANOVA469

Hypotheses, Notation, and Steps for Performing for the Two-Way ANOVA469

DATA BOX 12.B: Interpretation Qualification: Interactions Supercede Main Effects471

The Effects of Anxiety and Ordinal Position on Affiliation: A Detailed Example of a Two-Way ANOVA475

Knowledge Base475

DATA BOX 12.C: The General Linear Model for the Two-Way ANOVA476

Effect Size486

Estimated Omega-Squared (w2) for the Two-Way ANOVA487

Writing About the Results of a Two-Way ANOVA488

Coda: Beyond 2 × 2 Designs489

Knowledge Base490

PROJECT EXERCISE: More on Interpreting Interaction—Mean Polish and Displaying Residuals490

Looking Forward, Then Back495

Summary495

Key Terms495

Problems496

13 MEAN COMPARISION Ⅳ: ONE-VARIABLE REPEATED-MEASURES ANALYSIS OF VARIANCE499

One-Factor Repeated-Measures ANOVA501

Statistical Assumptions of the One-Way Repeated-Measures ANOVA502

Hypothesis, Notation, and Steps for Performing the One-Variable Repeated-Measures ANOVA503

DATA BOX 13.A: Cell Size Matters, But Keep the Cell Sizes Equal, Too508

Tukey's HSD Revisited510

Effect Size and the Degree of Association Between the Independent Variable and Dependent Measure511

Writing About the Results of a One-Way Repeated-Measures Design512

Knowledge Base513

DATA BOX 13.B: Improved Methodology Leads to Improved Analysis—Latin Square Designs514

Mixed Design ANOVA: A Brief Conceptual Overview of Between-Within Research Design515

PROJECT EXERCISE: Repeated-Measures Designs: Awareness of Threats to Validity and Inference516

Looking Forward, Then Back518

Summary518

Key Terms519

Problems519

14 SOME NONPARAMETRIC STATISTICS FOR CATEGORICAL AND ORDINAL DATA523

How Do Nonparametric Tests Differ from Parametric Tests?525

Advantages of Using Nonparametric Statistical Tests Over Parametric Tests526

Choosing to Use a Nonparametric Test: A Guide for the Perplexed527

DATA BOX 14.A: The Nonparametric Bible for the Behavioral Sciences: Siegel and Castellan (1988)528

The Chi-Square (x2) Test for Categorical Data528

Statistical Assumptions of the Chi-Square529

The Chi-Square Test for One-Variable: Goodness-of-Fit529

The Chi-Square Test of Independence of Categorical Variables534

DATA BOX 14.B: A Chi-Square Test for Independence Shortcut for 2 × 2 Tables538

Supporting Statistics for the Chi-Square Test of Independence: Phi(?) and Cramer's V538

Writing About the Result of a Chi-Square Test for Independence539

DATA BOX 14.C: Research Using the Chi-Square Test to Analyze Data540

Knowledge Base541

Ordinal Data: A Brief Overview541

The Mann-Whitney U Test541

DATA BOX 14.D: Handling Tied Ranks in Ordinal Data544

Mann-Whitney U Test for Larger (Ns > 20) Samples: A Normal Approximation of the U Distribution546

Writing About the Results of the Mann-Whitney U Test547

The Wilcoxon Matched-Pairs Signed-Ranks Test547

DATA BOX 14.E: Even Null Results Must Be Written Up and Reported550

Writing About the Results of the Wilcoxon (T) Test551

The Spearman Rank Order Correlation Coefficient551

Writing About the Results of a Spearman rs Test554

Knowledge Base554

DATA BOX 14.F: Research Using An Ordinal Test to Analyze Data555

PROJECT EXERCISE: Survey Says—Using Nonparametric Tests on Data556

Looking Forward, Then Back558

Summary558

Key Terms559

Problems559

15 CONCLUSION: STATISTICS AND DATA ANALYSIS IN CONTEXT563

The Fuss Over Null Hypothesis Significance Tests564

Panel Recommendations: Wisdom from the APA Task Force on Statistical Inference565

Knowledge Base567

Statistics as Avoidable Ideology567

Reprise: Right Answers Are Fine, but Interpretation Matters More568

Linking Analysis to Research569

Do Something: Collect Some Data, Run a Study, Get Involved569

Knowing When to Say When: Seeking Statistical Help in the Future570

DATA BOX 15.A: Statistical Heuristics and Improving Inductive Reasoning571

Data Analysis with Computers: The Tools Perspective Revisited572

Knowledge Base573

Thinking Like a Behavioral Scientist: Educational, Social, and Ethical Implications of Statistics and Data Analysis573

DATA BOX 15.B: Recurring Problems with Fraudulent, False, or Misleading Data Analysis: The Dracula Effect576

Conclusion578

PROJECT EXERCISE: A Checklist for Reviewing Published Research or Planning a Study578

Looking Forward, Then Back580

Summary580

Key Terms581

Problems581