Statistics for the behavioral sciences

This book not only teaches students the basic skills for analyzing data but also helps them become intelligent consumers of scientific information. Praised for its real-life applications, the text tells students when to use a particular statistic, why they should use it, and how the statistic should be computed and interpreted.

Preface	p. xv
To the Student	p. xxi
Part 1 Statistical Preliminaries	p. 1
Chapter 1 Introduction and Mathematical Preliminaries	p. 2
1.1 The Study of Statistics	p. 2
1.2 Research in the Behavioral Sciences	p. 4
1.3 Variables	p. 5
1.4 Measurement	p. 6
1.5 Discrete and Continuous Variables	p. 14
1.6 Populations and Samples	p. 16
Box 1.1 Biased Sampling	p. 17
1.7 Descriptive and Inferential Statistics	p. 18
1.8 The Concept of Probability	p. 19
1.9 Mathematical Preliminaries: A Review	p. 20
1.10 Statistics and Computers	p. 28
Summary	p. 29
Chapter 2 Frequency and Probability Distributions	p. 34
2.1 Frequency Distributions for Quantitative Variables: Ungrouped Scores	p. 34
2.2 Frequency Distributions for Quantitative Variables: Grouped Scores	p. 38
2.3 Frequency Distributions for Qualitative Variables	p. 41
2.4 Outliers	p. 42
2.5 Frequency Graphs	p. 43
2.6 Misleading Graphs	p. 51
2.7 Graphs of Relative Frequencies, Percentages, Cumulative Frequencies, and Cumulative Relative Frequencies	p. 52
2.8 Probability Distributions	p. 53
2.9 Empirical and Theoretical Distributions	p. 56
2.10 Method of Presentation	p. 57
2.11 Examples from the Literature	p. 59
Summary	p. 63
Chapter 3 Measures of Central Tendency and Variability	p. 67
3.1 Measures of Central Tendency for Quantitative Variables	p. 68
3.2 Measures of Variability for Quantitative Variables	p. 78
3.3 Computational Formula for the Sum of Squares	p. 83
3.4 Relationship Between Central Tendency and Variability	p. 85
3.5 Graphs of Central Tendency and Variability	p. 86
3.6 Measures of Central Tendency and Variability for Qualitative Variables	p. 89
3.7 Skewness and Kurtosis	p. 90
3.8 Sample Versus Population Notation	p. 91
3.9 Method of Presentation	p. 91
3.10 Example from the Literature	p. 92
Summary	p. 95
Chapter 4 Percentiles, Percentile Ranks, Standard Scores, and the Normal Distribution	p. 100
4.1 Percentiles and Percentile Ranks	p. 101
4.2 Standard Scores	p. 105
4.3 Standard Scores and the Normal Distribution	p. 109
4.4 Standard Scores and the Shape of the Distribution	p. 113
4.5 Method of Presentation	p. 113
Summary	p. 120
Appendix 4.1 The Normal Distribution Formula	p. 121
Chapter 5 Pearson Correlation and Regression: Descriptive Aspects	p. 125
5.1 Use of Pearson Correlation	p. 125
5.2 The Linear Model	p. 126
5.3 The Pearson Correlation Coefficient	p. 130
5.4 Correlation and Causation	p. 138
5.5 Interpreting the Magnitude of a Correlation Coefficient	p. 139
5.6 Regression	p. 140
5.7 Additional Issues Associated with the Use of Correlation and Regression	p. 145
Summary	p. 153
Chapter 6 Probability	p. 157
6.1 Probabilities of Simple Events	p. 159
6.2 Conditional Probabilities	p. 160
6.3 Joint Probabilities	p. 161
6.4 Adding Probabilities	p. 162
6.5 Relationships Among Probabilities	p. 162
6.6 Sampling with Versus Without Replacement	p. 164
Box 6.1 Beliefs and Probability Theory	p. 165
6.7 Counting Rules	p. 166
6.8 The Binomial Expression	p. 169
Summary	p. 176
Chapter 7 Estimation and Sampling Distributions	p. 181
7.1 Finite Versus Infinite Populations	p. 181
7.2 Estimation of the Population Mean	p. 182
7.3 Estimation of the Population Variance and Standard Deviation	p. 184
7.4 Degrees of Freedom	p. 187
7.5 Sampling Distribution of the Mean and the Central Limit Theorem	p. 188
Box 7.1 Polls and Random Samples	p. 191
7.6 Types of Sampling Distributions	p. 197
Summary	p. 202
Chapter 8 Hypothesis Testing: Inferences About a Single Mean	p. 205
8.1 A Simple Analogy for Principles of Hypothesis Testing	p. 205
8.2 Statistical Inference and the Normal Distribution: The One-Sample z Test	p. 206
8.3 Defining Expected and Unexpected Results	p. 210
8.4 Failing to Reject Versus Accepting the Null Hypothesis	p. 211
8.5 Type I and Type II Errors	p. 212
8.6 Effects of Alpha and Sample Size on the Power of Statistical Tests	p. 214
8.7 Statistical and Real-World Significance	p. 216
8.8 Directional Versus Nondirectional Tests	p. 216
8.9 Statistical Inference Using Estimated Standard Errors: The One-Sample t Test	p. 219
8.10 Confidence Intervals	p. 225
8.11 Method of Presentation	p. 229
8.12 Examples from the Literature	p. 231
Summary	p. 233
Part 2 The Analysis of Bivariate Relationships	p. 239
Chapter 9 Research Design and Statistical Preliminaries for Analyzing Bivariate Relationships	p. 240
9.1 Principles of Research Design: Statistical Implications	p. 240
Box 9.1 Confounding and Disturbance Variables	p. 247
9.2 Selecting the Appropriate Statistical Test to Analyze a Relationship: A Preview	p. 251
Summary	p. 255
Chapter 10 Independent Groups t Test	p. 259
10.1 Use of the Independent Groups t Test	p. 259
10.2 Inference of a Relationship Using the Independent Groups t Test	p. 261
10.3 Strength of the Relationship	p. 271
10.4 Nature of the Relationship	p. 280
10.5 Methodological Considerations	p. 281
10.6 Numerical Example	p. 281
10.7 Planning an Investigation Using the Independent Groups t Test	p. 284
10.8 Method of Presentation	p. 286
10.9 Examples from the Literature	p. 287
Summary	p. 294
Chapter 11 Correlated Groups t Test	p. 302
11.1 Use of the Correlated Groups t Test	p. 302
11.2 Inference of a Relationship Using the Correlated Groups t Test	p. 303
11.3 Strength of the Relationship	p. 308
11.4 Nature of the Relationship	p. 311
11.5 Methodological Considerations	p. 311
11.6 Power of Correlated Groups Versus Independent Groups t Tests	p. 312
11.7 Numerical Example	p. 314
11.8 Planning an Investigation Using the Correlated Groups t Test	p. 316
11.9 Method of Presentation	p. 317
11.10 Examples from the Literature	p. 318
Summary	p. 321
Appendix 11.1 Computational Procedures for the Nullified Score Approach	p. 322
Chapter 12 One-Way Between-Subjects Analysis of Variance	p. 329
12.1 Use of One-Way Between-Subjects Analysis of Variance	p. 329
12.2 Inference of a Relationship Using One-Way Between-Subjects Analysis of Variance	p. 330
12.3 Relationship of the F Test to the t Test	p. 344
12.4 Strength of the Relationship	p. 344
12.5 Nature of the Relationship	p. 345
12.6 Unstandardized Effect Sizes and Confidence Intervals	p. 349
12.7 Methodological Considerations	p. 350
12.8 Numerical Example	p. 350
12.9 Planning an Investigation Using One-Way Between-Subjects Analysis of Variance	p. 354
12.10 Method of Presentation	p. 354
12.11 Examples from the Literature	p. 356
Summary	p. 360
Appendix 12.1 Rationale for the Degrees of Freedom	p. 361
Chapter 13 One-Way Repeated Measures Analysis of Variance	p. 369
13.1 Use of One-Way Repeated Measures Analysis of Variance	p. 369
13.2 Inference of a Relationship Using One-Way Repeated Measures Analysis of Variance	p. 371
13.3 Strength of the Relationship	p. 380
13.4 Nature of the Relationship	p. 381
13.5 Unstandardized Effect Size and Confidence Intervals	p. 383
13.6 Methodological Considerations	p. 383
13.7 Numerical Example	p. 385
13.8 Planning an Investigation Using One-Way Repeated Measures Analysis of Variance	p. 388
13.9 Method of Presentation	p. 389
13.10 Examples from the Literature	p. 390
Summary	p. 395
Appendix 13.1 Determining the Nature of the Relationship Under Sphericity Violations	p. 395
Chapter 14 Pearson Correlation and Regression: Inferential Aspects	p. 402
14.1 Use of Pearson Correlation	p. 402
14.2 Inference of a Relationship Using Pearson Correlation	p. 403
14.3 Strength of the Relationship	p. 407
14.4 Confidence Intervals for the Correlation Coefficient	p. 407
14.5 Nature of the Relationship	p. 408
14.6 Planning an Investigation Using Pearson Correlation	p. 408
14.7 Method of Presentation for Pearson Correlation	p. 408
14.8 Examples from the Literature	p. 409
14.9 Regression	p. 411
14.10 Numerical Example	p. 414
14.11 Method of Presentation for Regression	p. 418
Summary	p. 423
Appendix 14.1 Testing Null Hypotheses Other Than [rho] = 0	p. 423
Appendix 14.2 Confidence Intervals for the Correlation Coefficient	p. 425
Chapter 15 Chi-Square Test	p. 433
15.1 Use of the Chi-Square Test	p. 433
15.2 Two-Way Contingency Tables	p. 434
15.3 Chi-Square Tests of Independence and Homogeneity	p. 435
15.4 Inference of a Relationship Using the Chi-Square Test	p. 435
15.5 2 x 2 Tables	p. 441
15.6 Strength of the Relationship	p. 442
15.7 Nature of the Relationship	p. 443
15.8 Methodological Considerations	p. 444
15.9 Numerical Example	p. 445
15.10 Use of Quantitative Variables in the Chi-Square Test	p. 446
15.11 Planning an Investigation Using the Chi-Square Test	p. 447
15.12 Method of Presentation	p. 448
15.13 Examples from the Literature	p. 449
15.14 Chi-Square Goodness-of-Fit Test	p. 451
Summary	p. 455
Appendix 15.1 Determining the Nature of the Relationship Using a Modified Bonferroni Procedure	p. 456
Chapter 16 Nonparametric Statistics	p. 463
16.1 Rank Scores	p. 464
16.2 Nonparametric Statistics and Outliers	p. 466
16.3 Analysis of Ranked Data Using Parametric Formulas	p. 467
16.4 Rank Tests for Two Independent Groups	p. 467
16.5 Rank Test for Two Correlated Groups	p. 471
16.6 Rank Test for Three or More Independent Groups	p. 474
16.7 Rank Test for Three or More Correlated Groups	p. 477
16.8 Rank Test for Correlation	p. 480
16.9 Examples from the Literature	p. 483
Summary	p. 486
Appendix 16.1 Corrections for Ties for Nonparametric Rank Tests	p. 486
Part 3 Additional Topics	p. 495
Chapter 17 Two-Way Between-Subjects Analysis of Variance	p. 496
17.1 Factorial Designs	p. 497
17.2 Use of Two-Way Between-Subjects Analysis of Variance	p. 498
17.3 The Concepts of Main Effects and Interactions	p. 499
17.4 Inference of Relationships Using Two-Way Between-Subjects Analysis of Variance	p. 506
17.5 Strength of the Relationships	p. 514
17.6 Nature of the Relationships	p. 515
17.7 Methodological Considerations	p. 518
17.8 Numerical Example	p. 518
17.9 Unequal Sample Sizes	p. 526
17.10 Planning an Investigation Using Two-Way Between-Subjects Analysis of Variance	p. 527
17.11 Method of Presentation	p. 529
17.12 Examples from the Literature	p. 531
Summary	p. 536
Chapter 18 Overview and Extension: Selecting the Appropriate Statistical Test for Analyzing Bivariate Relationships and Procedures for More Complex Designs	p. 544
18.1 Selecting the Appropriate Statistical Test for Analyzing Bivariate Relationships	p. 544
18.2 Case I: The Relationship Between Two Qualitative Variables	p. 545
18.3 Case II: The Relationship Between a Qualitative Independent Variable and a Quantitative Dependent Variable	p. 545
18.4 Case III: The Relationship Between a Quantitative Independent Variable and a Qualitative Dependent Variable	p. 549
18.5 Case IV: The Relationship Between Two Quantitative Variables	p. 549
18.6 Procedures for More Complex Designs	p. 550
18.7 Alternative Approaches to Null Hypothesis Testing	p. 553
Summary	p. 554
Appendix A Table of Random Numbers	p. 559
Appendix B Proportions of Scores in a Normal Distribution	p. 562
Appendix C Factorials	p. 572
Appendix D Critical Values for the t Distribution	p. 573
Appendix E Power and Sample Size	p. 575
Appendix F Critical Values for the F Distribution	p. 599
Appendix G Studentized Range Values (q)	p. 603
Appendix H Critical Values for Pearson r	p. 606
Appendix I Fisher's Transformation of Pearson r(r')	p. 608
Appendix J Critical Values for the Chi-Square Distribution	p. 610
Appendix K Critical Values for the Mann-Whitney U Test	p. 612
Appendix L Critical Values for the Wilcoxon Signed-Rank Test	p. 615
Appendix M Critical Values for Spearman r	p. 617
Appendix N Formulas for Unbiased Estimators of Proportion of Explained Variance	p. 619
Answers to Selected Exercises	p. 620
Glossary of Major Symbols	p. 639
References	p. 644
Index	p. 651
Credits	p. 658

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