Cited by more than 300 scholars, Statistical Reasoning in the Behavioral Sciences continues to provide streamlined resources and easy-to-understand information on statistics in the behavioral sciences and related fields, including psychology, education, human resources management, and sociology. Students and professionals in the behavioral sciences will develop an understanding of statistical logic and procedures, the properties of statistical devices, and the importance of the assumptions underlying statistical tools. This revised and updated edition continues to follow the recommendations of the APA Task Force on Statistical Inference and greatly expands the information on testing hypotheses about single means. The Seventh Edition moves from a focus on the use of computers in statistics to a more precise look at statistical software. The “Point of Controversy” feature embedded throughout the text provides current discussions of exciting and hotly debated topics in the field. Readers will appreciate how the comprehensive graphs, tables, cartoons and photographs lend vibrancy to all of the material covered in the text.

Table of Contents:
PREFACE vii ABOUT THE BOOK AND AUTHORS x 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, 5 1.5 Scales of Measurement, 6 1.6 Scales of Measurement and Problems of Statistical Treatment, 8 1.7 Do Statistics Lie?, 9 Point of Controversy: Are Statistical Procedures Necessary?, 11 1.8 Some Tips on Studying Statistics, 12 1.9 Statistics and Computers, 12 1.10 Summary, 13 2 FREQUENCY DISTRIBUTIONS, PERCENTILES, AND PERCENTILE RANKS 16 2.1 Organizing Qualitative Data, 16 2.2 Grouped Scores, 18 2.3 How to Construct a Grouped Frequency Distribution, 19 2.4 Apparent versus Real Limits, 21 2.5 The Relative Frequency Distribution, 21 2.6 The Cumulative Frequency Distribution, 22 2.7 Percentiles and Percentile Ranks, 24 2.8 Computing Percentiles from Grouped Data, 25 2.9 Computation of Percentile Rank, 28 2.10 Summary, 28 3 GRAPHIC REPRESENTATION OF FREQUENCY DISTRIBUTIONS 32 3.1 Basic Procedures, 32 3.2 The Histogram, 33 3.3 The Frequency Polygon, 34 3.4 Choosing between a Histogram and a Polygon, 35 3.5 The Bar Diagram and the Pie Chart, 37 3.6 The Cumulative Percentage Curve, 39 3.7 Factors Affecting the Shape of Graphs, 40 3.8 Shape of Frequency Distributions, 42 3.9 Summary, 43 4 CENTRAL TENDENCY 46 4.1 The Mode, 46 4.2 The Median, 47 4.3 The Mean, 48 4.4 Properties of the Mode, 49 4.5 Properties of the Mean, 50 Point of Controversy: Is It Permissible to Calculate the Mean for Tests in the Behavioral Sciences?, 51 4.6 Properties of the Median, 52 4.7 Measures of Central Tendency in Symmetrical and Asymmetrical Distributions, 53 4.8 The Effects of Score Transformations, 54 4.9 Summary, 55 5 VARIABILITY AND STANDARD (z) SCORES 58 5.1 The Range and Semi-Interquartile Range, 58 5.2 Deviation Scores, 60 5.3 Deviational Measures: The Variance, 61 5.4 Deviational Measures: The Standard Deviation, 62 5.5 Calculation of the Variance and Standard Deviation: Raw-Score Method, 63 5.6 Calculation of the Standard Deviation with SPSS, 64 Point of Controversy: Calculating the Sample Variance: Should We Divide by n or (n − 1)?, 67 5.7 Properties of the Range and Semi-Interquartile Range, 68 5.8 Properties of the Standard Deviation, 68 5.9 How Big Is a Standard Deviation?, 69 5.10 Score Transformations and Measures of Variability, 69 5.11 Standard Scores (z Scores), 70 5.12 A Comparison of z Scores and Percentile Ranks, 73 5.13 Summary, 74 6 STANDARD SCORES AND THE NORMAL CURVE 78 6.1 Historical Aspects of the Normal Curve, 78 6.2 The Nature of the Normal Curve, 81 6.3 Standard Scores and the Normal Curve, 81 6.4 The Standard Normal Curve: Finding Areas When the Score Is Known, 83 6.5 The Standard Normal Curve: Finding Scores When the Area Is Known, 86 6.6 The Normal Curve as a Model for Real Variables, 88 6.7 The Normal Curve as a Model for Sampling Distributions, 88 Point of Controversy: How Normal Is the Normal Curve?, 89 6.8 Summary, 89 7 CORRELATION 92 7.1 Some History, 93 7.2 Graphing Bivariate Distributions: The Scatter Diagram, 95 7.3 Correlation: A Matter of Direction, 96 7.4 Correlation: A Matter of Degree, 98 7.5 Understanding the Meaning of Degree of Correlation, 99 7.6 Formulas for Pearson’s Coefficient of Correlation, 100 7.7 Calculating r from Raw Scores, 101 7.8 Calculating r with SPSS, 103 7.9 Spearman’s Rank-Order Correlation Coefficient, 106 7.10 Correlation Does Not Prove Causation, 107 7.11 The Effects of Score Transformations, 110 7.12 Cautions Concerning Correlation Coefficients, 110 7.13 Summary, 114 8 PREDICTION 118 8.1 The Problem of Prediction, 118 8.2 The Criterion of Best Fit, 120 Point of Controversy: Least-Squares Regression versus the Resistant Line, 121 8.3 The Regression Equation: Standard-Score Form, 122 8.4 The Regression Equation: Raw-Score Form, 123 8.5 Error of Prediction: The Standard Error of Estimate, 125 8.6 An Alternative (and Preferred) Formula for SYX, 127 8.7 Calculating the “Raw-Score” Regression Equation and Standard Error of Estimate with SPSS, 128 8.8 Error in Estimating Y from X, 130 8.9 Cautions Concerning Estimation of Predictive Error, 132 8.10 Prediction Does Not Prove Causation, 133 8.11 Summary, 133 9 INTERPRETIVE ASPECTS OF CORRELATION AND REGRESSION 136 9.1 Factors Influencing r: Degree of Variability in Each Variable, 136 9.2 Interpretation of r: The Regression Equation I, 137 9.3 Interpretation of r: The Regression Equation II, 139 9.4 Interpretation of r : Proportion of Variation in Y Not Associated with Variation in X, 140 9.5 Interpretation of r: Proportion of Variance in Y Associated with Variation in X, 142 9.6 Interpretation of r: Proportion of Correct Placements, 144 9.7 Summary, 145 10 PROBABILITY 147 10.1 Defining Probability, 148 10.2 A Mathematical Model of Probability, 149 10.3 Two Theorems in Probability, 150 10.4 An Example of a Probability Distribution: The Binomial, 151 10.5 Applying the Binomial, 153 10.6 Probability and Odds, 155 10.7 Are Amazing Coincidences Really That Amazing?, 155 10.8 Summary, 156 11 RANDOM SAMPLING AND SAMPLING DISTRIBUTIONS 160 11.1 Random Sampling, 161 11.2 Using a Table of Random Numbers, 163 11.3 The Random Sampling Distribution of the Mean: An Introduction, 164 11.4 Characteristics of the Random Sampling Distribution of the Mean, 166 11.5 Using the Sampling Distribution of X to Determine the Probability for Different Ranges of Values of X, 168 11.6 Random Sampling without Replacement, 173 11.7 Summary, 173 12 INTRODUCTION TO STATISTICAL INFERENCE: TESTING HYPOTHESES ABOUT A SINGLE MEAN (z) 175 12.1 Testing a Hypothesis about a Single Mean, 176 12.2 The Null and Alternative Hypotheses, 176 12.3 When Do We Retain and When Do We Reject the Null Hypothesis?, 178 12.4 Review of the Procedure for Hypothesis Testing, 178 12.5 Dr. Brown’s Problem: Conclusion, 178 12.6 The Statistical Decision, 180 12.7 Choice of HA: One-Tailed and Two-Tailed Tests, 182 12.8 Review of Assumptions in Testing Hypotheses about a Single Mean, 183 Point of Controversy: The Single-Subject Research Design, 184 12.9 Summary, 185 13 TESTING HYPOTHESES ABOUT A SINGLE MEAN WHEN 𝜎 IS UNKNOWN (t) 187 13.1 Estimating the Standard Error of the Mean When 𝜎 Is Unknown, 187 13.2 The t Distribution, 189 13.3 Characteristics of Student’s Distribution of t, 191 13.4 Degrees of Freedom and Student’s Distribution of t, 192 13.5 An Example: Has the Violent Content of Television Programs Increased?, 193 13.6 Calculating t from Raw Scores, 196 13.7 Calculating t with SPSS, 198 13.8 Levels of Significance versus p-Values, 200 13.9 Summary, 202 14 INTERPRETING THE RESULTS OF HYPOTHESIS TESTING: EFFECT SIZE, TYPE I AND TYPE II ERRORS, AND POWER 205 14.1 A Statistically Significant Difference versus a Practically Important Difference, 205 Point of Controversy: The Failure to Publish “Nonsignificant” Results, 206 14.2 Effect Size, 207 14.3 Errors in Hypothesis Testing, 210 14.4 The Power of a Test, 212 14.5 Factors Affecting Power: Difference between the True Population Mean and the Hypothesized Mean (Size of Effect), 212 14.6 Factors Affecting Power: Sample Size, 213 14.7 Factors Affecting Power: Variability of the Measure, 214 14.8 Factors Affecting Power: Level of Significance (𝛼), 214 14.9 Factors Affecting Power: One-Tailed versus Two-Tailed Tests, 214 14.10 Calculating the Power of a Test, 216 Point of Controversy: Meta-Analysis, 217 14.11 Estimating Power and Sample Size for Tests of Hypotheses about Means, 218 14.12 Problems in Selecting a Random Sample and in Drawing Conclusions, 220 14.13 Summary, 221 15 TESTING HYPOTHESES ABOUT THE DIFFERENCE BETWEEN TWO INDEPENDENT GROUPS 224 15.1 The Null and Alternative Hypotheses, 224 15.2 The Random Sampling Distribution of the Difference between Two Sample Means, 225 15.3 Properties of the Sampling Distribution of the Difference between Means, 228 15.4 Determining a Formula for t, 228 15.5 Testing the Hypothesis of No Difference between Two Independent Means: The Dyslexic Children Experiment, 231 15.6 Use of a One-Tailed Test, 234 15.7 Calculation of t with SPSS, 234 15.8 Sample Size in Inference about Two Means, 237 15.9 Effect Size, 237 15.10 Estimating Power and Sample Size for Tests of Hypotheses about the Difference between Two Independent Means, 241 15.11 Assumptions Associated with Inference about the Difference between Two Independent Means, 242 15.12 The Random-Sampling Model versus the Random-Assignment Model, 243 15.13 Random Sampling and Random Assignment as Experimental Controls, 244 15.14 Summary, 245 16 TESTING FOR A DIFFERENCE BETWEEN TWO DEPENDENT (CORRELATED) GROUPS 249 16.1 Determining a Formula for t, 250 16.2 Degrees of Freedom for Tests of No Difference between Dependent Means, 251 16.3 An Alternative Approach to the Problem of Two Dependent Means, 251 16.4 Testing a Hypothesis about Two Dependent Means: Does Text Messaging Impair Driving?, 252 16.5 Calculating t with SPSS, 254 16.6 Effect Size, 257 16.7 Power, 258 16.8 Assumptions When Testing a Hypothesis about the Difference between Two Dependent Means, 259 16.9 Problems with Using the Dependent-Samples Design, 259 16.10 Summary, 261 17 INFERENCE ABOUT CORRELATION COEFFICIENTS 264 17.1 The Random Sampling Distribution of r, 264 17.2 Testing the Hypothesis That 𝜌 = 0, 265 17.3 Fisher’s z′ Transformation, 267 17.4 Strength of Relationship, 268 17.5 A Note about Assumptions, 268 17.6 Inference When Using Spearman’s rS, 269 17.7 Summary, 269 18 AN ALTERNATIVE TO HYPOTHESIS TESTING: CONFIDENCE INTERVALS 271 18.1 Examples of Estimation, 272 18.2 Confidence Intervals for 𝜇X, 273 18.3 The Relation between Confidence Intervals and Hypothesis Testing, 276 18.4 The Advantages of Confidence Intervals, 276 18.5 Random Sampling and Generalizing Results, 277 18.6 Evaluating a Confidence Interval, 278 Point of Controversy: Objectivity and Subjectivity in Inferential Statistics: Bayesian Statistics, 279 18.7 Confidence Intervals for 𝜇X − 𝜇Y , 280 18.8 Sample Size Required for Confidence Intervals of 𝜇X and 𝜇X − 𝜇Y , 283 18.9 Confidence Intervals for 𝜌, 285 18.10 Where Are We in Statistical Reform?, 286 18.11 Summary, 287 19 TESTING FOR DIFFERENCES AMONG THREE OR MORE GROUPS: ONE-WAY ANALYSIS OF VARIANCE (AND SOME ALTERNATIVES) 289 19.1 The Null Hypothesis, 291 19.2 The Basis of One-Way Analysis of Variance: Variation within and Between Groups, 291 19.3 Partition of the Sums of Squares, 293 19.4 Degrees of Freedom, 295 19.5 Variance Estimates and the F Ratio, 296 19.6 The Summary Table, 297 19.7 Example: Does Playing Violent Video Games Desensitize People to Real-Life Aggression?, 298 19.8 Comparison of t and F, 301 19.9 Raw-Score Formulas for Analysis of Variance, 302 19.10 Calculation of ANOVA for Independent Measures with SPSS, 303 19.11 Assumptions Associated with ANOVA, 306 19.12 Effect Size, 306 19.13 ANOVA and Power, 307 19.14 Post Hoc Comparisons, 308 19.15 Some Concerns about Post Hoc Comparisons, 310 19.16 An Alternative to the F Test: Planned Comparisons, 310 19.17 How to Construct Planned Comparisons, 311 19.18 Analysis of Variance for Repeated Measures, 314 19.19 Calculation of ANOVA for Repeated Measures with SPSS, 319 19.20 Summary, 321 20 FACTORIAL ANALYSIS OF VARIANCE: THE TWO-FACTOR DESIGN 326 20.1 Main Effects, 327 20.2 Interaction, 329 20.3 The Importance of Interaction, 331 20.4 Partition of the Sums of Squares for Two-Way ANOVA, 332 20.5 Degrees of Freedom, 336 20.6 Variance Estimates and F Tests, 337 20.7 Studying the Outcome of Two-Factor Analysis of Variance, 338 20.8 Effect Size, 340 20.9 Calculation of Two-Factor ANOVA with SPSS, 341 20.10 Planned Comparisons, 342 20.11 Assumptions of the Two-Factor Design and the Problem of Unequal Numbers of Scores, 343 20.12 Mixed Two-Factor Within-Subjects Design, 344 20.13 Calculation of the Mixed Two-Factor Within-Subjects Design with SPSS, 348 20.14 Summary, 349 21 CHI-SQUARE AND INFERENCE ABOUT FREQUENCIES 353 21.1 The Chi-Square Test for Goodness of Fit, 353 21.2 Chi-Square (𝜒2) as a Measure of the Difference between Observed and Expected Frequencies, 355 21.3 The Logic of the Chi-Square Test, 356 21.4 Interpretation of the Outcome of a Chi-Square Test, 358 21.5 Different Hypothesized Proportions in the Test for Goodness of Fit, 358 21.6 Effect Size for Goodness-of-Fit Problems, 359 21.7 Assumptions in the Use of the Theoretical Distribution of Chi-Square, 360 21.8 Chi-Square as a Test for Independence between Two Variables, 360 21.9 Finding Expected Frequencies in a Contingency Table, 362 21.10 Calculation of 𝜒2 and Determination of Significance in a Contingency Table, 363 21.11 Measures of Effect Size (Strength of Association) for Tests of Independence, 364 Point of Controversy: Yates’ Correction for Continuity, 365 21.12 Power and the Chi-Square Test of Independence, 367 21.13 Summary, 368 22 SOME (ALMOST) ASSUMPTION-FREE TESTS 371 22.1 The Null Hypothesis in Assumption-Freer Tests, 372 22.2 Randomization Tests, 372 22.3 Rank-Order Tests, 374 22.4 The Bootstrap Method of Statistical Inference, 375 22.5 An Assumption-Freer Alternative to the t Test of a Difference between Two Independent Groups: The Mann–Whitney U Test, 376 Point of Controversy: A Comparison of the t Test and the Mann–Whitney U Test with Real-World Distributions, 379 22.6 An Assumption-Freer Alternative to the t Test of a Difference Between Two Dependent Groups: The Sign Test, 380 22.7 Another Assumption-Freer Alternative to the t Test of a Difference Between Two Dependent Groups: The Wilcoxon Signed-Ranks Test, 382 22.8 An Assumption-Freer Alternative to the One-Way ANOVA for Independent Groups: The Kruskal–Wallis Test, 384 22.9 An Assumption-Freer Alternative to ANOVA for Repeated Measures: Friedman’s Rank Test for Correlated Samples, 387 22.10 Summary, 389 EPILOGUE 392 APPENDIX A REVIEW OF BASIC MATHEMATICS 396 APPENDIX B LIST OF SYMBOLS 405 APPENDIX C ANSWERS TO PROBLEMS 408 APPENDIX D STATISTICAL TABLES 424 Table A: Areas under the Normal Curve Corresponding to Given Values of z, 424 Table B: The Binomial Distribution, 429 Table C: Random Numbers, 432 Table D: Student’s t Distribution, 434 Table E: The F Distribution, 436 Table F: The Studentized Range Statistic, 440 Table G: Values of the Correlation Coefficient Required for Different Levels of Significance When H0∶ 𝜌 = 0, 441 Table H: Values of Fisher’s z′ for Values of r, 443 Table I: The 𝜒2 Distribution, 444 Table J: Critical One-Tail Values of ΣRX for the Mann–Whitney U Test, 445 Table K: Critical Values for the Smaller of R+ or R− for the Wilcoxon Signed-Ranks Test, 447 REFERENCES 448 INDEX 454