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Copyright, iv
Preface, vii
About the Authors, xi
Contents, xiii
Chapter 1. Introduction, 1
1.1. Descriptive Statistics, 3
1.2. Inferential Statistics, 3
1.3. Our Concern: Applied Statistics, 4
1.4. Variables and Constants, 6
1.5. Scales of Measurement, 7
1.6. Scales of Measurement and Problems of Statistical Treatment, 10
1.7. Do Statistics Lie?, 11
1.8. Some Tips on Studying Statistics, 14
1.9. Summary, 15
Chapter 2. Frequency Distributions, Percentiles, and Percentile Ranks, 19
2.1. Organizing Qualitative Data, 21
2.2. Grouped Scores, 21
2.3. How to Construct a Grouped Frequency Distribution, 23
2.4. Apparent versus Real Limits, 24
2.5. The Relative Frequency Distribution, 26
2.6. The Cumulative Frequency Distribution, 27
2.7. Percentiles and Percentile Ranks, 28
2.8. Computing Percentiles from Grouped Data, 29
2.9. Computation of Percentile Rank, 32
2.10. Summary, 32
Chapter 3. Graphic Representation of Frequency Distributions, 37
3.1. Basic Procedures, 38
3.2. The Histogram, 39
3.3. The Frequency Polygon, 40
3.4. Choosing between a Histogram and a Polygon, 41
3.5. The Bar Diagram and the Pie Chart, 43
3.6. The Cumulative Percentage Curve, 45
3.7. Factors Affecting the Shape of Graphs, 47
3.8. Shape of Frequency Distributions, 50
3.9. Summary, 50
Chapter 4. Central Tendency, 55
4.1. The Mode, 56
4.2. The Median, 56
4.3. The Mean, 58
4.4. Properties of the Mode, 59
4.5. Properties of the Mean, 60
4.6. Properties of the Median, 62
4.7. Measures of Central Tendency in Symmetrical and Asymmetrical Distributions, 64
4.8. The Effects of Score Transformations, 65
4.9. Summary, 65
Chapter 5. Variability and Standard (z) Scores, 69
5.1. The Range and Semi-Interquartile Range, 71
5.2. Deviation Scores, 72
5.3. Deviational Measures: The Variance, 73
5.4. Deviational Measures: The Standard Deviation, 74
5.5. Calculation of the Variance and Standard Deviation: Raw-Score Method, 75
5.6. Properties of the Range and Semi-Interquartile Range, 76
5.7. Properties of the Standard Deviation, 78
5.8. How Big Is a Standard Deviation?, 78
5.9. Score Transformations and Measures of Variability, 79
5.10. Standard Scores (z Scores), 80
5.11. A Comparison of z Scores and Percentile Ranks, 83
5.12. Summary, 83
Chapter 6. Standard Scores and the Normal Curve, 89
6.1. Historical Aspects of the Normal Curve, 90
6.2. The Nature of the Normal Curve, 92
6.3. Standard Scores and the Normal Curve, 94
6.4. The Standard Normal Curve: Finding Areas When the Score Is Known, 94
6.5. The Standard Normal Curve: Finding Scores When the Area Is Known, 97
6.6. The Normal Curve as a Model for Real Variables, 99
6.7. The Normal Curve as a Model for Sampling Distributions, 100
6.8. Summary, 100
Chapter 7. Correlation, 105
7.1. Some History, 107
7.2. Graphing Bivariate Distributions: The Scatter Diagram, 107
7.3. Correlation: A Matter of Direction, 111
7.4. Correlation: A Matter of Degree, 112
7.5. Understanding the Meaning of Degree of Correlation, 113
7.6. Formulas for Pearson’s Coefficient of Correlation, 115
7.7. Calculating r from Raw Scores, 118
7.8. Spearman’s Rank-Order Correlation Coefficient, 120
7.9. Correlation Does Not Prove Causation, 121
7.10. The Effects of Score Transformations, 124
7.11. Cautions Concerning Correlation Coefficients, 124
7.12. Summary, 128
Chapter 8. Prediction, 133
8.1. The Problem of Prediction, 134
8.2. The Criterion of Best Fit, 136
8.3. The Regression Equation: Standard-Score Form, 138
8.4. The Regression Equation: Raw-Score Form, 139
8.5. Error of Prediction: The Standard Error of Estimate, 141
8.6. An Alternative (and Preferred) Formula for S_YX, 143
8.7. Error in Estimating Y from X, 143
8.8. Cautions Concerning Estimation of Predictive Error, 145
8.9. Summary, 146
Chapter 9. Interpretive Aspects of Correlation and Regression, 151
9.1. Factors Influencing r: Degree of Variability in Each Variable, 152
9.2. Interpretation of r: The Regression Equation I, 152
9.3. Interpretation of r: The Regression Equation II, 154
9.4. Interpretation of r: Proportion of Variation in Y Not Associated with Variation in X, 156
9.5. Interpretation of r: Proportion of Variation in Y Associated with Variation in X, 158
9.6. Interpretation of r: Proportion of Correct Placements, 160
9.7. Summary, 161
Chapter 10. Probability, 165
10.1. Defining Probability, 166
10.2. A Mathematical Model of Probability, 168
10.3. Two Theorems in Probability, 168
10.4. An Example of a Probability Distribution: The Binomial, 170
10.5. Applying the Binomial, 172
10.6. Are Amazing Coincidences Really That Amazing?, 174
10.7. Summary, 175
Chapter 11. Random Sampling and Sampling Distributions, 179
11.1. Random Sampling, 181
11.2. Using a Table of Random Numbers, 182
11.3. The Random Sampling Distribution of the Mean: An Introduction, 183
11.4. Characteristics of the Random Sampling Distribution of the Mean, 186
11.5. Using the Sampling Distribution of X̄ to Determine the Probability for Different Ranges of Values of X̄, 189
11.6. Random Sampling Without Replacement, 192
11.7. Summary, 192
Chapter 12. Introduction to Statistical Inference: Testing Hypotheses about Single Means (z and t), 195
12.1. Testing a Hypothesis about a Single Mean, 197
12.2. The Null and Alternative Hypotheses, 197
12.3. When Do We Retain and When Do We Reject the Null Hypothesis?, 198
12.4. Review of the Procedure for Hypothesis Testing, 199
12.5. Dr. Brown’s Problem: Conclusion, 199
12.6. The Statistical Decision, 201
12.7. Choice of H_A: One-Tailed and Two-Tailed Tests, 203
12.8. Review of Assumptions in Testing Hypotheses about a Single Mean, 205
12.9. Estimating the Standard Error of the Mean When σ Is Unknown, 205
12.10. The t Distribution, 209
12.11. Characteristics of Student’s Distribution of t, 210
12.12. Degrees of Freedom and Student’s Distribution of t, 212
12.13. An Example: Professor Dyett’s Question, 213
12.14. Computing t from Raw Scores, 215
12.15. Levels of Significance versus p-Values, 218
12.16. Summary, 219
Chapter 13. Interpreting the Results of Hypothesis Testing: Effect Size, Type I and Type II Errors, and Power, 225
13.1. A Statistically Significant Difference versus a Practically Important Difference, 226
13.2. Effect Size, 228
13.3. Errors in Hypothesis Testing, 230
13.4. The Power of a Test, 233
13.5. Factors Affecting Power: Discrepancy between the True Population Mean and the Hypothesized Mean (Size of Effect), 233
13.6. Factors Affecting Power: Sample Size, 234
13.7. Factors Affecting Power: Variability of the Measure, 235
13.8. Factors Affecting Power: Level of Significance (α), 235
13.9. Factors Affecting Power: One-Tailed versus Two-Tailed Tests, 236
13.10. Calculating the Power of a Test, 237
13.11. Estimating Power and Sample Size for Tests of Hypotheses about Means, 240
13.12. Problems in Selecting a Random Sample and in Drawing Conclusions, 242
13.13. Summary, 243
Chapter 14. Testing Hypotheses about the Difference between Two Independent Groups, 247
14.1. The Null and Alternative Hypotheses, 248
14.2. The Random Sampling Distribution of the Difference between Two Sample Means, 249
14.3. Properties of the Sampling Distribution of the Difference between Means, 251
14.4. Determining a Formula for t, 252
14.5. Testing the Hypothesis of No Difference between Two Independent Means: The Dyslexic Children Experiment, 255
14.6. Use of a One-Tailed Test, 257
14.7. Sample Size in Inference about Two Means, 258
14.8. Effect Size, 258
14.9. Estimating Power and Sample Size for Tests of Hypotheses about the Difference between Two Independent Means, 263
14.10. Assumptions Associated with Inference about the Difference between Two Independent Means, 265
14.11. The Random-Sampling Model versus the Random-Assignment Model, 266
14.12. Random Sampling and Random Assignment as Experimental Controls, 267
14.13. Summary, 268
Chapter 15. Testing for a Difference between Two Dependent (Correlated) Groups, 273
15.1. Determining a Formula for t, 274
15.2. Degrees of Freedom for Tests of No Difference between Dependent Means, 275
15.3. An Alternative Approach to the Problem of Two Dependent Means, 276
15.4. Testing a Hypothesis about Two Dependent Means, 277
15.5. Effect Size, 280
15.6. Power, 281
15.7. Assumptions When Testing a Hypothesis about the Difference between Two Dependent Means, 282
15.8. Problems with Using the Dependent-Samples Design, 282
15.9. Summary, 283
Chapter 16. Inference about Correlation Coefficients, 287
16.1. The Random Sampling Distribution of r, 288
16.2. Testing the Hypothesis that ρ = 0, 289
16.3. Fisher’s z′ Transformation, 290
16.4. Strength of Relationship, 292
16.5. A Note about Assumptions, 292
16.6. Inference When Using Spearman’s r_S, 292
16.7. Summary, 293
Chapter 17. An Alternative to Hypothesis Testing: Confidence Intervals, 295
17.1. Examples of Estimation, 297
17.2. Confidence Intervals for μ_X, 297
17.3. The Relation between Confidence Intervals and Hypothesis Testing, 300
17.4. The Advantages of Confidence Intervals, 301
17.5. Random Sampling and Generalizing Results, 302
17.6. Evaluating a Confidence Interval, 303
17.7. Confidence Intervals for μ_X – μ_Y, 306
17.8. Sample Size Required for Confidence Intervals of μ_X and μ_X – μ_Y, 309
17.9. Confidence Intervals for ρ, 311
17.10. Summary, 312
Chapter 18. Chi-Square and Inference about Frequencies, 315
18.1. The Chi-Squre Test for Goodness of Fit, 316
18.2. Chi-Square (χ²) as a Measure of the Difference between Expected and Observed Frequencies, 318
18.3. The Logic of the Chi-Square Test, 319
18.4. Interpretation of the Outcome of a Chi-Square Test, 320
18.5. Different Hypothesized Proportions in the Test for Goodness of Fit, 321
18.6. Effect Size for Goodness-of-Fit Problems, 322
18.7. Assumptions in the Use of the Theoretical Distribution of Chi-Square, 322
18.8. Chi-Square as a Test for Independence between Two Variables, 323
18.9. Finding Expected Frequencies in a Contingency Table, 325
18.10. Calculation of χ² and Determination of Significance in a Contingency Table, 326
18.11. Measures of Effect Size (Strength of Association) for Tests of Independence, 327
18.12. Power and the Chi-Square Test of Independence, 329
18.13. Summary, 330
Chapter 19. Testing for Differences among Three or More Groups: One-Way Analysis of Variance (and Some Alternatives), 335
19.1. The Null Hypothesis, 336
19.2. The Basis of One-Way Analysis of Variance: Variation within and between Groups, 337
19.3. Partition of the Sums of Squares, 338
19.4. Degrees of Freedom, 341
19.5. Variance Estimates and the F Ratio, 342
19.6. The Summary Table, 344
19.7. Example, 344
19.8. Comparison of t and F, 347
19.9. Raw-Score Formulas for Analysis of Variance, 347
19.10. Assumptions Associated with ANOVA, 350
19.11. Effect Size, 350
19.12. ANOVA and Power, 352
19.13. Post Hoc Comparisons, 352
19.14. Some Concerns about Post Hoc Comparisons, 354
19.15. An Alternative to the F Test: Planned Comparisons, 354
19.16. How to Construct Planned Comparisons, 355
19.17. Analysis of Variance for Repeated Measures, 358
19.18. Summary, 365
Chapter 20. Factorial Analysis of Variance: The Two-Factor Design for Independent Groups, 369
20.1. Main Effects, 371
20.2. Interaction, 373
20.3. The Importance of Interaction, 375
20.4. Partition of the Sums of Squares for Two-Way ANOVA, 376
20.5. Degrees of Freedom, 381
20.6. Variance Estimates and F Tests, 381
20.7. Studying the Outcome of Two-Factor Analysis of Variance, 383
20.8. Effect Size, 384
20.9. Planned Comparisons, 385
20.10. Assumptions of the Two-Factor Design and the Problem of Unequal Numbers of Scores, 386
20.11. Summary, 386
Chapter 21. Some (Almost) Assumption-Free Tests, 389
21.1. The Null Hypothesis in Assumption-Freer Tests, 390
21.2. Randomization Tests, 390
21.3. Rank-Order Tests, 393
21.4. An Assumption-Freer Alternative to the t Test of a Difference between Two Independent Groups: The Mann-Whitney U Test, 394
21.5. An Assumption-Freer Alternative to the t Test of a Difference between Two Dependent Groups: The Sign Test, 399
21.6. Another Assumption-Freer Alternative to the t Test of a Difference between Two Dependent Groups: The Wilcoxon Signed-Ranks Test, 401
21.7. An Assumption-Freer Alternative to One-Way ANOVA for Independent Groups: The Kruskal–Wallis Test, 403
21.8. An Assumption-Freer Alternative to ANOVA for Repeated Measures: Friedman’s Rank Test for Correlated Samples, 406
21.9. Summary, 408
Epilogue: The Realm of Statistics, 411
Appendix A. Review of Basic Mathematics, 415
Appendix B. List of Symbols, 425
Appendix C. Answers to Problems, 429
Appendix D. Statistical Tables, 445
Table A: Areas under the Normal Curve Corresponding to Given Values of z, 446
Table B: The Binomial Distribution, 451
Table C: Random Numbers, 455
Table D: Student’s t Distribution, 458
Table E: The F Distribution, 460
Table F: The Studentized Range Statistic, 464
Table G: Values of the Correlation Coefficient Required for Different Levels of Significance When H₀: ρ = 0, 465
Table H: Values of Fisher’s z′ for Values of r, 467
Table I: The χ² Distribution, 468
Table J: Critical One-Tail Values of ΣR_X for the Mann-Whitney U Test, 469
Table K: Critical Values for the Smaller of R₊ or R_- for the Wilcoxon Signed-Ranks Test, 471
REFERENCES, 473
INDEX, 481
Useful Formulas, EM-1

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