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