STATISTICS AND DATA ANAL:YSIS FOR THE BEHAVIORAL:SCIENCESPDF电子书下载

1 INTRODUCTION: STATISTICS AND DATA ANALYSIS AS TOOLS FOR RESEARCHERS 3

2 PROCESS OF RESEARCH IN PSYCHOLOGY AND RELATED FIELDS 45

3 FREQUENCY DISTRIBUTIONS, GRAPHING, AND DATA DISPLAY 85

4 DESCRIPTIVE STATISTICS: CENTRAL TENDENCY AND VARIABILITY 133

5 STANDARD SCORES AND THE NORMAL DISTRIBUTION 177

6 CORRELATION 205

7 LINEAR REGRESSION 241

8 PROBABILITY 273

9 INFERENTIAL STATISTICS: SAMPLING DISTRIBUTIONS AND HYPOTHESIS TESTING 315

10 MEAN COMPARISON Ⅰ: THE t TEST 365

11 MEAN COMPARISON Ⅱ: ONE-VARIABLE ANALYSIS OF VARIANCE 411

12 MEAN COMPARISON Ⅲ: TWO-VARIABLE ANALYSIS OF VARIANCE 459

13 MEAN COMPARISON Ⅳ: ONE-VARIABLE REPEATED-MEASURES ANALYSIS OF VARIANCE 499

14 SOME NONPARAMETRIC STATISTICS FOR CATEGORICAL AND ORDINAL DATA 523

15 CONCLUSION: STATISTICS AND DATA ANALYSIS IN CONTEXT 563

1 INTRODUCTION: STATISTICS AND DATA ANALYSIS AS TOOLS FOR RESEARCHERS 3

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

Tools for Inference: David L.'s Problem 5

College Choice 6

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

Statistics Is the Science of Data, Not Mathematics 8

Statistics, Data Analysis, and the Scientific Method 9

Inductive and Deductive Reasoning 10

Populations and Samples 12

Descriptive and Inferential Statistics 16

DATA BOX 1.B: Reactions to the David L. Problem 18

Knowledge Base 19

Discontinuous and Continuous Variables 20

DATA BOX 1.c: Rounding and Continuous Variables 22

Writing About Data: Overview and Agenda 23

Scales of Measurement 24

Nominal Scales 25

Ordinal Scales 26

Interval Scales 27

Ratio Scales 28

Writing About Scales 29

Knowledge Base 31

Overview of Statistical Notation 31

What to Do When: Mathematical Rules of Priority 34

DATA BOX 1.D: The Size of Numbers is Relative 38

Mise en Place 39

About Calculators 39

Knowledge Base 40

PROJECT EXERCISE: Avoiding Statisticophobia 40

Looking Forward, Then Back 41

Summary 42

Key Terms 42

Problems 42

2 PROCESS OF RESEARCH IN PSYCHOLOGY AND RELATED FIELDS 45

The Research Loop of Experimentation: An Overview of the Research Process 45

Populations and Samples Revisited: The Role of Randomness 48

Distinguishing Random Assignment from Random Sampling 48

Some Other Randomizing Procedures 50

Sampling Error 52

Knowledge Base 53

DATA BOX 2.A: Recognizing Randomness, Imposing Order 54

Independent and Dependent Variables 54

Types of Dependent Measures 58

Closing or Continuing the Research Loop? 60

DATA BOX 2.B: Variable Distinctions: Simple, Sublime, and All Too Easily Forgotten 61

The Importance of Determining Causality 61

DATA BOX 2.C: The “Hot Hand in Basketball” and the Misrepresentation of Randomness 62

Operational Definitions in Behavioral Research 63

Writing Operational Definitions 64

Knowledge Base 64

Reliability and Validity 65

Reliability 66

Validity 67

Knowledge Base 69

Research Designs 70

Correlational Research 70

Experiments 72

Quasi-experiments 74

DATA BOX 2.D: Quasi-experimentation in Action: What to Do Without Random Assignment or a Control Group 75

Knowledge Base 76

PROJECT EXERCISE: Using a Random Numbers Table 77

Looking Forward, Then Back 81

Summary 81

Key Terms 82

Problems 82

3 FREQUENCY DISTRIBUTIONS, GRAPHING, AND DATA DISPLAY 85

What is a Frequency Distribution? 87

DATA BOX 3.A: Dispositional Optimism and Health: A Lot About the LOT 88

Proportions and Percentages 90

Grouping Frequency Distributions 92

True Limits and Frequency Distributions 95

Knowledge Base 96

Graphing Frequency Distributions 97

Bar Graphs 98

Histograms 99

Frequency Polygons 100

Misrepresenting Relationships: Biased or Misleading Graphs 102

New Alternatives for Graphing Data: Exploratory Data Analysis 104

Stem and Leaf Diagrams 105

DATA BOX 3.B: Biased Graphical Display—Appearances Can Be Deceiving 106

Tukey's Tallies 108

Knowledge Base 109

Envisioning the Shape of Distributions 111

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

DATA BOX 3.D: Elegant Information—Napoleon's Ill-fated March to Moscow 114

Percentiles and Percentile Ranks 115

Cumulative Frequency 116

Cumulative Percentage 117

Calculating Percentile Rank 118

Reversing the Process: Finding Scores from Percentile Ranks 119

Exploring Data: Calculating the Middle Percentiles and Quartiles 120

Writing About Percentiles 122

Knowledge Base 123

Constructing Tables and Graphs 123

Less is More: Avoiding Chartjunk and Tableclutter, and Other Suggestions 124

American Psychological Association (APA) Style Guidelines for Data Display 125

PROJECT EXERCISE: Discussing the Benefits of Accurate but Persuasive Data Display 126

Looking Forward, Then Back 127

Summary 128

Key Terms 129

Problems 129

4 DESCRIPTIVE STATISTICS: CENTRAL TENDENCY AND VARIABILITY 133

Why Represent Data By Central Tendency 134

The Mean: The Behavioral Scientist's Statistic of Choice 136

DATA BOX 4.A: How Many Are There? And Where Did They Come 138

From? Proper Use of N and n 138

Calculating Means from Ungrouped and Grouped Data 138

Caveat Emptor: Sensitivity to Extreme Scores 140

Weighted Means: An Approach for Determining Averages of Different-Sized Groups 142

DATA BOX 4.B: Self-Judgment Under Uncertainty—Being Average is Sometimes OK 143

The Median 144

The Mode 145

The Utility of Central Tendency 147

Shapes of Distributions and Central Tendency 147

When to Use Which Measure of Central Tendency 148

Writing About Central Tendency 149

Knowledge Base 150

Understanding Variability 151

The Range 153

The Interquartile and the Semi-Interquartile Range 153

Variance and Standard Deviation 155

Sample Variance and Standard Deviation 157

Homogeneity and Heterogeneity: Understanding the Standard Deviations of Different Distributions 159

Calculating Variance and Standard Deviation from a Data Array 160

Population Variance and Standard Deviation 161

Looking Ahead: Biased and Unbiased Estimators of Variance and Standard Deviation 162

DATA BOX 4.c: Avoid Computation Frustration: Get to Know Your Calculator 165

Knowledge Base 165

Factors Affecting Variability 166

Writing About Range, Variance, and Standard Deviation 168

DATA BOX 4.D: Sample Size and Variability—The Hospital Problem 169

PROJECT EXERCISE: Proving the Least Squares Principle for the Mean 170

Looking Forward, Then Back 171

Summary 172

Key Terms 173

Problems 173

5 STANDARD SCORES AND THE NORMAL DISTRIBUTION 177

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 Accounts 180

Why Standardize Measures? 181

The z Score: A Conceptual Introduction 182

Formulas for Calculating z Scores 185

The Standard Normal Distribution 186

Standard Deviation Revisited: The Area Under the Normal Curve 187

Application: Comparing Performance on More than One Measure 188

Knowledge Base 189

Working with z Scores and the Normal Distribution 190

Finding Percentile Ranks with z Scores 191

Further Examples of Using z Scores to Identify Areas Under the Normal Curve 192

DATA BOX 5.C: Intelligence, Standardized IQ Scores, and the Normal Distribution 194

A Further Transformed Score: The T Score 196

Writing About Standard Scores and the Normal Distribution 197

Knowledge Base 198

Looking Ahead: Probability, z Scores, and the Normal Distribution 198

PROJECT EXERCISE: Understanding the Recentering of Scholastic Aptitude Test Scores 199

Looking Forward, Then Back 201

Summary 202

Key Terms 202

Problems 202

6 CORRELATION 205

Association, Causation, and Measurement 206

Galton, Pearson, and the Index of Correlation 207

A Brief But Essential Aside: Correlation Does Not Imply Causation 207

The Pearson Correlation Coefficient 209

Conceptual Definition of the Pearson r 209

DATA BOX 6.A: Mood as Misbegotten: Correlating Predictors with Mood States 213

Calculating the Pearson r 216

Interpreting Correlation 221

Magnitude of r 222

Coefficients of Determination and Nondetermination 222

Factors Influencing r 224

Writing About Correlational Relationships 226

Knowledge Base 227

Correlation as Consistency and Reliability 228

DATA BOX 6.B: Personality, Cross-Situational Consistency, and Correlation 228

Other Types of Reliability Defined 229

A Brief Word About Validity 229

DATA BOX 6.c: Examining a Correlation Matrix: A Start for Research 230

What to Do When: A Brief, Conceptual Guide to Other Measures of Association 231

DATA BOX 6.D: Perceived Importance of Scientific Topics and Evaluation Bias 232

PROJECT EXERCISE: Identifying Predictors of Your Mood 233

Looking Forward, Then Back 237

Summary 237

Key Terms 238

Problems 238

7 LINEAR REGRESSION 241

Simple Linear Regression 242

The z Score Approach to Regression 242

Computational Approaches to Regression 243

The Method of Least Squares for Regression 245

Knowledge Base 249

DATA BOX 7.A: Predicting Academic Success 250

Residual Variation and the Standard Error of Estimate 251

DATA BOX 7.B: The Clinical and the Statistical: Intuition Versus Prediction 253

Assumptions Underlying the Standard Error of Estimate 253

Partitioning Variance: Explained and Unexplained Variation 256

A Reprise for the Coefficients of Determination and Nondetermination 257

Proper Use of Regression: A Brief Recap 258

Knowledge Base 258

Regression to the Mean 259

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

Regression as a Research Tool 261

Other Applications of Regression in the Behavioral Sciences 262

Writing About Regression Results 263

Multivariate Regression: A Conceptual Overview 263

PROJECT EXERCISE: Perceiving Risk and Judging the Frequency of Deaths 264

Looking Forward, Then Back 268

Summary 268

Key Terms 269

Problems 269

8 PROBABILITY 273

The Gambler's Fallacy or Randomness Revisited 275

Probability: A Theory of Outcomes 277

Classical Probability Theory 277

DATA BOX B.A: “I Once Knew a Man Who&”: Beware Man-Who Statistics 278

Probability's Relationship to Proportion and Percentage 281

DATA BOX 8.B: Classical Probability and Classic Probability Examples 282

Probabilities Can Be Obtained from Frequency Distributions 283

Knowledge Base 283

DATA BOX 8.c: A Short History of Probability 284

Calculating Probabilities Using the Rules for Probability 285

The Addition Rule for Mutually Exclusive and Nonmutually Exclusive Events 285

The Multiplication Rule for Independent and Conditional Probabilities 287

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

Multiplication Rule for Dependent Events 293

Knowledge Base 293

Using Probabilities with the Standard Normal Distribution: z Scores Revisited 294

Determining Probabilities with the Binomial Distribution: An Overview 299

Working with the Binomial Distribution 300

Approximating the Standard Normal Distribution with the Binomial Distribution 301

DATA BOX 8.E: Control, Probability, and When the Stakes Are High 304

Knowledge Base 305

p Values: A Brief Introduction 305

Writing About Probability 306

PROJECT EXERCISE: Flipping Coins and the Binomial Distribution 307

Looking Forward, Then Back 310

Summary 310

Key Terms 311

Problems 311

9 INFERENTIAL STATISTICS: SAMPLING DISTRIBUTIONS AND HYPOTHESIS TESTING 315

Samples, Population, and Hypotheses: Links to Estimation and Experimentation 316

Point Estimation 317

Statistical Inference and Hypothesis Testing 318

The Distribution of Sample Means 319

Expected Value and Standard Error 320

The Central Limit Theorem 322

Law of Large Numbers Redux 322

DATA BOX 9.A: The Law of Small Numbers Revisited 323

Standard Error and Sampling Error in Depth 324

Estimating the Standard Error of the Mean 324

Standard Error of the Mean: A Concrete Example Using Population Parameters 326

Defining Confidence Intervals Using the Standard Error of the Mean 327

DATA BOX 9.B: Standard Error as an Index of Stability and Reliability of Means 328

Knowledge Base 329

DATA BOX 9.C: Representing Standard Error Graphically 330

Asking and Testing Focused Questions: Conceptual Rationale for Hypotheses 331

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

Directional and Nondirectional Hypotheses 333

The Null and the Experimental Hypothesis 333

Statistical Significance: A Concrete Account 336

DATA BOX 9.E: Distinguishing Between Statistical and Practical Significance 337

Critical Values: Establishing Criteria for Rejecting the Null Hypothesis 338

One- and Two-Tailed Tests 340

Degrees of Freedom 341

DATA BOX 9.F: When the Null Hypothesis is Rejected—Evaluating Results with the MAGIC Criteria 342

Knowledge Base 343

Single Sample Hypothesis Testing: The z Test and the Significance of r 343

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 Ⅱ 349

Statistical Power and Effect Size 351

Effect Size 354

Writing About Hypotheses and the Results of Statistical Tests 355

Knowledge Base 357

PROJECT EXERCISE: Thinking About Statistical Significance in the Behavioral Science Literature 357

Looking Forward, Then Back 360

Summary 360

Key Terms 362

Problems 362

10 MEAN COMPARISON I: THE t TEST 365

Recapitulation: Why Compare Means? 367

The Relationship Between the t and the z Distributions 368

The t Distribution 368

Assumptions Underlying the t Test 369

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

Hypothesis Testing with t: One-Sample Case 372

Confidence Intervals for the One-Sample t Test 375

DATA BOX 10.B: The Absolute Value of t 376

Power Issues and the One-Sample t Test 377

Knowledge Base 377

Hypothesis Testing with Two Independent Samples 378

Standard Error Revised: Estimating the Standard Error of the Difference Between Means 379

Comparing Means: A Conceptual Model and an Aside for Future Statistical Tests 383

The t Test for Independent Groups 384

DATA BOX 10.C: Language and Reporting Results, or (Too) Great Expectations 388

Effect Size and the t Test 388

Characterizing the Degree of Association Between the Independent Variable and the Dependent Measure 389

DATA BOX 10.D: Small Effects Can Be Impressive Too 390

Knowledge Base 392

Hypothesis Testing with Correlated Research Designs 393

The Statistical Advantage of Correlated Groups Designs: Reducing Error Variance 395

The t Test for Correlated Groups 396

Calculating Effect Size for Correlated Research Designs 399

A Brief Overview of Power Analysis: Thinking More Critically About Research and Data Analysis 400

Knowledge Base 402

PROJECT EXERCISE: Planning for Data Analysis: Developing a Before and After Data Collection Analysis Plan 402

Looking Forward, Then Back 405

Summary 405

Key Terms 406

Problems 406

11 MEAN COMPARISON Ⅱ: ONE-VARIABLE ANALYSIS OF VARIANCE 411

Overview of the Analysis of Variance 413

Describing the F Distribution 417

Comparing the ANOVA to the t Test: Shared Characteristics and Assumptions 418

Problematic Probabilities: Multiple t Tests and the Risk of Type I Error 420

DATA BOX 11.A: R. A. Fischer: Statistical Genius and Vituperative Visionary 422

How is the ANOVA Distinct from Prior Statistical Tests? Some Advantages 423

Omnibus Test: Comparing More than Two Means Simultaneously 423

DATA BOX 1 1.B: Linguistically Between a Rock and Among Hard Places 424

Experimentwise Error: Protecting Against Type I Error 424

Causality and Complexity 425

Knowledge Base 426

One-Factor Analysis of Variance 426

Identifying Statistical Hypotheses for the ANOVA 427

Some Notes on Notation and the ANOVA's Steps 429

DATA BOX 1 1.C: Yet Another Point of View on Variance: The General Linear Model 431

One-Way ANOVA from Start to Finish: An Example with Data 431

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

Tukey's Honestly Significant Difference Test 440

Effect Size for the F Ratio 442

Estimating the Degree of Association Between the Independent Variable and the Dependent Measure 443

DATA BOX 11.D: A Variance Paradox—Explaining Variance Due to Skill or Baseball is Life 444

Writing About the Results of a One-Way ANOVA 445

Knowledge Base 446

An Alternative Strategy for Comparing Means: A Brief Introduction to Contrast Analysis 447

PROJECT EXERCISE: Writing and Exchanging Letters About the ANOVA 451

Looking Forward, Then Back 452

Summary 453

Key Terms 454

Problems 454

12 MEAN COMPARISON Ⅲ: TWO-VARIABLE ANALYSIS OF VARIANCE 459

Overview of Complex Research Designs: Life Beyond Manipulating One Variable 460

Two-Factor Analysis of Variance 461

DATA BOX 12.A: Thinking Factorially 463

Reading Main Effects and the Concept of Interaction 465

Statistical Assumptions of the Two-Factor ANOVA 469

Hypotheses, Notation, and Steps for Performing for the Two-Way ANOVA 469

DATA BOX 12.B: Interpretation Qualification: Interactions Supercede Main Effects 471

The Effects of Anxiety and Ordinal Position on Affiliation: A Detailed Example of a Two-Way ANOVA 475

Knowledge Base 475

DATA BOX 12.C: The General Linear Model for the Two-Way ANOVA 476

Effect Size 486

Estimated Omega-Squared (w2) for the Two-Way ANOVA 487

Writing About the Results of a Two-Way ANOVA 488

Coda: Beyond 2 × 2 Designs 489

Knowledge Base 490

PROJECT EXERCISE: More on Interpreting Interaction—Mean Polish and Displaying Residuals 490

Looking Forward, Then Back 495

Summary 495

Key Terms 495

Problems 496

13 MEAN COMPARISION Ⅳ: ONE-VARIABLE REPEATED-MEASURES ANALYSIS OF VARIANCE 499

One-Factor Repeated-Measures ANOVA 501

Statistical Assumptions of the One-Way Repeated-Measures ANOVA 502

Hypothesis, Notation, and Steps for Performing the One-Variable Repeated-Measures ANOVA 503

DATA BOX 13.A: Cell Size Matters, But Keep the Cell Sizes Equal, Too 508

Tukey's HSD Revisited 510

Effect Size and the Degree of Association Between the Independent Variable and Dependent Measure 511

Writing About the Results of a One-Way Repeated-Measures Design 512

Knowledge Base 513

DATA BOX 13.B: Improved Methodology Leads to Improved Analysis—Latin Square Designs 514

Mixed Design ANOVA: A Brief Conceptual Overview of Between-Within Research Design 515

PROJECT EXERCISE: Repeated-Measures Designs: Awareness of Threats to Validity and Inference 516

Looking Forward, Then Back 518

Summary 518

Key Terms 519

Problems 519

14 SOME NONPARAMETRIC STATISTICS FOR CATEGORICAL AND ORDINAL DATA 523

How Do Nonparametric Tests Differ from Parametric Tests? 525

Advantages of Using Nonparametric Statistical Tests Over Parametric Tests 526

Choosing to Use a Nonparametric Test: A Guide for the Perplexed 527

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

The Chi-Square (x2) Test for Categorical Data 528

Statistical Assumptions of the Chi-Square 529

The Chi-Square Test for One-Variable: Goodness-of-Fit 529

The Chi-Square Test of Independence of Categorical Variables 534

DATA BOX 14.B: A Chi-Square Test for Independence Shortcut for 2 × 2 Tables 538

Supporting Statistics for the Chi-Square Test of Independence: Phi(?) and Cramer's V 538

Writing About the Result of a Chi-Square Test for Independence 539

DATA BOX 14.C: Research Using the Chi-Square Test to Analyze Data 540

Knowledge Base 541

Ordinal Data: A Brief Overview 541

The Mann-Whitney U Test 541

DATA BOX 14.D: Handling Tied Ranks in Ordinal Data 544

Mann-Whitney U Test for Larger (Ns > 20) Samples: A Normal Approximation of the U Distribution 546

Writing About the Results of the Mann-Whitney U Test 547

The Wilcoxon Matched-Pairs Signed-Ranks Test 547

DATA BOX 14.E: Even Null Results Must Be Written Up and Reported 550

Writing About the Results of the Wilcoxon (T) Test 551

The Spearman Rank Order Correlation Coefficient 551

Writing About the Results of a Spearman rs Test 554

Knowledge Base 554

DATA BOX 14.F: Research Using An Ordinal Test to Analyze Data 555

PROJECT EXERCISE: Survey Says—Using Nonparametric Tests on Data 556

Looking Forward, Then Back 558

Summary 558

Key Terms 559

Problems 559

15 CONCLUSION: STATISTICS AND DATA ANALYSIS IN CONTEXT 563

The Fuss Over Null Hypothesis Significance Tests 564

Panel Recommendations: Wisdom from the APA Task Force on Statistical Inference 565

Knowledge Base 567

Statistics as Avoidable Ideology 567

Reprise: Right Answers Are Fine, but Interpretation Matters More 568

Linking Analysis to Research 569

Do Something: Collect Some Data, Run a Study, Get Involved 569

Knowing When to Say When: Seeking Statistical Help in the Future 570

DATA BOX 15.A: Statistical Heuristics and Improving Inductive Reasoning 571

Data Analysis with Computers: The Tools Perspective Revisited 572

Knowledge Base 573

Thinking Like a Behavioral Scientist: Educational, Social, and Ethical Implications of Statistics and Data Analysis 573

DATA BOX 15.B: Recurring Problems with Fraudulent, False, or Misleading Data Analysis: The Dracula Effect 576

Conclusion 578

PROJECT EXERCISE: A Checklist for Reviewing Published Research or Planning a Study 578

Looking Forward, Then Back 580

Summary 580

Key Terms 581

Problems 581