Statistical. Psychology

Transcription

1 SEVENTH у *i km m it* & П SB Й EDITION Statistical M e t h o d s for Psychology D a v i d C. Howell University of Vermont ; \ WADSWORTH f% CENGAGE Learning* Australia Biaall apan Korea Меяко Singapore -Spain United Kingdom United States

2 Contents Preface xvii About the Author Basic Concepts xxi Important Terms 2 Descriptive and Inferential Statistics Measurement Scales Using Computers 1.5 The Plan of the Book 9 9 Describing and Exploring Data Plotting Data 16 Histograms 18 Fitting Smooth Lines to Data Stem-and-Leaf Displays 24 Describing Distributions Notation 30 Measures of Central Tendency Measures of Variability 36 Boxplots: Graphical Representations of Dispersions and Extreme Scores Obtaining Measures of Central Tendency and Dispersion Using SPSS Percentiles, Quartiles, and Deciles 52 The Effect of Linear Transformations on Data 32 52

3 x Contents CHAPTER CHAPTER CHAPTER CHAPTER The Normal Distribution The Normal Distribution The Standard Normal Distribution 3.3 Using the Tables of the Standard Normal Distribution 3.4 Setting Probable Limits on an Observation 3.5 Assessing Whether Data Are Normally Distributed 3.6 Measures Related to г Sampling Distributions and Hypothesis Testing Two Simple Examples Involving Course Evaluations and Rude Motorists 4.2 Sampling Distributions 4.3 Theory of Hypothesis Testing 4.4 The Null Hypothesis 4.5 Test Statistics and Their Sampling Distributions 4.6 Making Decisions About the Null Hypothesis 4.7 Type I and Type II Errors One- and Two-Tailed Tests What Does It Mean to Reject the Null Hypothesis? 4.10 An Alternative View of Hypothesis Testing 4.11 Effect Size 4.12 A Final Worked Example 4.13 Back to Course Evaluations and Rude Motorists Basic Concepts of Probability Probability 5.2 Basic Terminology and Rules Discrete versus Continuous Variables 5.4 Probability Distributions for Discrete Variables 5.5 Probability Distributions for Continuous Variables 5.6 Permutations and Combinations 5.7 Bayes' Theorem 5.8 The Binomial Distribution 5.9 Using the Binomial Distribution to Test Hypotheses 5.10 The Multinomial Distribution Categorical Data and Chi-Square The Chi-Square Distribution 6.2 The Chi-Square Goodness-of-Fit Test One-Way Classification Two Classification Variables: Contingency Table Analysis 6.4 An Additional Example A 4 X 2 Design

4 Contents xi 6.5 Chi-Square for Ordinal Data Summary of the Assumptions of Chi-Square Dependent or Repeated Measurements One- and Two-Tailed Tests Likelihood Ratio Tests Mantel-Haenszel Statistic Effect Sizes A Measure of Agreement Writing Up the Results 167 CHAPTER 7 Hypothesis Tests Applied to Means Sampling Distribution of the Mean Testing Hypotheses About Means и Known Testing a Sample Mean When a Is Unknown The One-Sample t Test Hypothesis Tests Applied to Means Two Matched Samples Hypothesis Tests Applied to Means Two Independent Samples A Second Worked Example Heterogeneity of Variance: The Behrens-Fisher Problem Hypothesis Testing Revisited 216 CHAPTER 8 Power Factors Affecting the Power of a Test Effect Size Power Calculations for the One-Sample t Power Calculations for Differences Between Two Independent Means Power Calculations for Matched-Sample t Power Calculations in More Complex Designs The Use of G*Power to Simplify Calculations Retrospective Power Writing Up the Results of a Power Analysis 241 CHAPTER 9 Correlation and Regression Scatterplot The Relationship Between Stress and Health The Covariance The Pearson Product-Moment Correlation Coefficient (r) The Regression Line Other Ways of Fitting a Line to Data The Accuracy of Prediction Assumptions Underlying Regression and Correlation 264

5 xii Contents 9.9 Confidence Limits on Y A Computer Example Showing the Role of Test-Taking Skills Hypothesis Testing One Final Example The Role of Assumptions in Correlation and Regression Factors That Affect the Correlation Power Calculation for Pearson's r 283 CHAPTER 10 Alternative Correlational Techniques Point-Biserial Correlation and Phi: Pearson Correlations by Another Name Biserial and Tetrachoric Correlation: Non-Pearson Correlation Coefficients Correlation Coefficients for Ranked Data Analysis of Contingency Tables with Ordered Variables Kendall's Coefficient of Concordance (W) 309 CHAPTER 11 Simple Analysis of Variance An Example The Underlying Model The Logic of the Analysis of Variance Calculations in the Analysis of Variance Writing Up the Results Computer Solutions Unequal Sample Sizes Violations of Assumptions Transformations Fixed versus Random Models The Size of an Experimental Effect Power Computer Analyses 354 CHAPTER 12 Multiple Comparisons Among Treatment Means Error Rates Multiple Comparisons in a Simple Experiment on Morphine Tolerance A Priori Comparisons Confidence Intervals and Effect Sizes for Contrasts Reporting Results Post Hoc Comparisons Comparison of the Alternative Procedures Which Test? 398

6 Contents xiii 12.9 Computer Solutions Trend Analysis 402 CHAPTER 13 Factorial Analysis of Variance An Extension of the Eysenck Study Structural Models and Expected Mean Squares Interactions Simple Effects Analysis of Variance Applied to the Effects of Smoking Multiple Comparisons Power Analysis for Factorial Experiments Expected Mean Squares and Alternative Designs Measures of Association and Effect Size Reporting the Results Unequal Sample Sizes Higher-Order Factorial Designs A Computer Example 453 CHAPTER 14 Repeated-Measures Designs The Structural Model F Ratios The Covariance Matrix Analysis of Variance Applied to Relaxation Therapy Contrasts and Effect Sizes in Repeated Measures Designs Writing Up the Results One Between-Subjects Variable and One Within-Subjects Variable Two Between-Subjects Variables and One Within-Subjects Variable Two Within-Subjects Variables and One Between-Subjects Variable Intraclass Correlation Other Considerations Mixed Models for Repeated-Measures Designs 499 CHAPTER 15 Multiple Regression Multiple Linear Regression Using Additional Predictors Standard Errors and Tests of Regression Coefficients Residual Variance Distribution Assumptions The Multiple Correlation Coefficient 532

7 xiv Contents 15.7 Geometric Representation of Multiple Regression Partial and Semipartial Correlation Suppressor Variables Regression Diagnostics Constructing a Regression Equation The "Importance" of Individual Variables Using Approximate Regression Coefficients Mediating and Moderating Relationships Logistic Regression 561 CHAPTER 16 Analyses of Variance and Covariance as General Linear Models The General Linear Model One-Way Analysis of Variance Factorial Designs Analysis of Variance with Unequal Sample Sizes The One-Way Analysis of Covariance Computing Effect Sizes in an Analysis of Covariance Interpreting an Analysis of Covariance Reporting the Results of an Analysis of Covariance The Factorial Analysis of Covariance Using Multiple Covariates Alternative Experimental Designs 621 CHAPTER 17 Log-Linear Analysis Two-Way Contingency Tables Model Specification Testing Models Odds and Odds Ratios Treatment Effects (Lambda) Three-Way Tables Deriving Models Treatment Effects 652 CHAPTER 18 Resampling and Nonparametric Approaches to Data Bootstrapping as a General Approach Bootstrapping with One Sample Resampling with Two Paired Samples Resampling with Two Independent Samples 668

8 Contents xv 18.5 Bootstrapping Confidence Limits on a Correlation Coefficient Wilcoxon's Rank-Sum Test Wilcoxon's Matched-Pairs Signed-Ranks Test The Sign Test Kraskal-Wallis One-Way Analysis of Variance Friedman's Rank Test for к Correlated Samples 684 Appendices 690 References 724 Answers to Exercises 735 Index 757