3.13 CONTRASTS AND POST‐HOCS 3.14 POST‐HOC TESTS 3.15 SAMPLE SIZE AND POWER FOR ANOVA: ESTIMATION WITH R AND G*POWER 3.16 FIXED EFFECTS ONE‐WAY ANALYSIS OF VARIANCE IN R: MATHEMATICS ACHIEVEMENT AS A FUNCTION OF TEACHER 3.17 ANALYSIS OF VARIANCE VIA R’s lm 3.18 KRUSKAL–WALLIS TEST IN R AND THE MOTIVATION BEHIND NONPARAMETRIC TESTS 3.19 ANOVA IN SPSS: ACHIEVEMENT AS A FUNCTION OF TEACHER 3.20 CHAPTER SUMMARY AND HIGHLIGHTS REVIEW EXERCISES Further Discussion and Activities
10 4 FACTORIAL ANALYSIS OF VARIANCE 4.1 WHAT IS FACTORIAL ANALYSIS OF VARIANCE? 4.2 THEORY OF FACTORIAL ANOVA: A DEEPER LOOK 4.3 COMPARING ONE‐WAY ANOVA TO TWO‐WAY ANOVA: CELL EFFECTS IN FACTORIAL ANOVA VERSUS SAMPLE EFFECTS IN ONE‐WAY ANOVA 4.4 PARTITIONING THE SUMS OF SQUARES FOR FACTORIAL ANOVA: THE CASE OF TWO FACTORS 4.5 INTERPRETING MAIN EFFECTS IN THE PRESENCE OF INTERACTIONS 4.6 EFFECT SIZE MEASURES 4.7 THREE‐WAY, FOUR‐WAY, AND HIGHER MODELS 4.8 SIMPLE MAIN EFFECTS 4.9 NESTED DESIGNS 4.10 ACHIEVEMENT AS A FUNCTION OF TEACHER AND TEXTBOOK: EXAMPLE OF FACTORIAL ANOVA IN R 4.11 INTERACTION CONTRASTS 4.12 CHAPTER SUMMARY AND HIGHLIGHTS REVIEW EXERCISES
11 5 INTRODUCTION TO RANDOM EFFECTS AND MIXED MODELS 5.1 WHAT IS RANDOM EFFECTS ANALYSIS OF VARIANCE? 5.2 THEORY OF RANDOM EFFECTS MODELS 5.3 ESTIMATION IN RANDOM EFFECTS MODELS 5.4 DEFINING NULL HYPOTHESES IN RANDOM EFFECTS MODELS 5.5 COMPARING NULL HYPOTHESES IN FIXED VERSUS RANDOM EFFECTS MODELS: THE IMPORTANCE OF ASSUMPTIONS 5.6 ESTIMATING VARIANCE COMPONENTS IN RANDOM EFFECTS MODELS: ANOVA, ML, REML ESTIMATORS 5.7 IS ACHIEVEMENT A FUNCTION OF TEACHER? ONE‐WAY RANDOM EFFECTS MODEL IN R 5.8 R ANALYSIS USING REML 5.9 ANALYSIS IN SPSS: OBTAINING VARIANCE COMPONENTS 5.10 Factorial Random Effects: A Two‐Way Model 5.11 FIXED EFFECTS VERSUS RANDOM EFFECTS: A WAY OF CONCEPTUALIZING THEIR DIFFERENCES 5.12 CONCEPTUALIZING THE TWO‐WAY RANDOM EFFECTS MODEL: THE MAKE‐UP OF A RANDOMLY CHOSEN OBSERVATION 5.13 SUMS OF SQUARES AND EXPECTED MEAN SQUARES FOR RANDOM EFFECTS: THE CONTAMINATING INFLUENCE OF INTERACTION EFFECTS 5.14 YOU GET WHAT YOU GO IN WITH: THE IMPORTANCE OF MODEL ASSUMPTIONS AND MODEL SELECTION 5.15 MIXED MODEL ANALYSIS OF VARIANCE: INCORPORATING FIXED AND RANDOM EFFECTS 5.16 MIXED MODELS IN MATRICES 5.17 MULTILEVEL MODELING AS A SPECIAL CASE OF THE MIXED MODEL: INCORPORATING NESTING AND CLUSTERING 5.18 CHAPTER SUMMARY AND HIGHLIGHTS Review Exercises
12 6 RANDOMIZED BLOCKS AND REPEATED MEASURES 6.1 WHAT IS A RANDOMIZED BLOCK DESIGN? 6.2 RANDOMIZED BLOCK DESIGNS: SUBJECTS NESTED WITHIN BLOCKS 6.3 THEORY OF RANDOMIZED BLOCK DESIGNS 6.4 TUKEY TEST FOR NONADDITIVITY 6.5 ASSUMPTIONS FOR THE COVARIANCE MATRIX 6.6 INTRACLASS CORRELATION 6.7 REPEATED MEASURES MODELS: A SPECIAL CASE OF RANDOMIZED BLOCK DESIGNS 6.8 INDEPENDENT VERSUS PAIRED‐SAMPLES t‐TEST 6.9 THE SUBJECT FACTOR: FIXED OR RANDOM EFFECT? 6.10 MODEL FOR ONE‐WAY REPEATED MEASURES DESIGN 6.11 ANALYSIS USING R: ONE‐WAY REPEATED MEASURES: LEARNING AS A FUNCTION OF TRIAL 6.12 ANALYSIS USING SPSS: ONE‐WAY REPEATED MEASURES: LEARNING AS A FUNCTION OF TRIAL 6.13 SPSS TWO‐WAY REPEATED MEASURES ANALYSIS OF VARIANCE MIXED DESIGN: ONE BETWEEN FACTOR, ONE WITHIN FACTOR 6.14 Chapter Summary and Highlights Review Exercises
13 7 LINEAR REGRESSION 7.1 BRIEF HISTORY OF REGRESSION 7.2 REGRESSION ANALYSIS AND SCIENCE: EXPERIMENTAL VERSUS CORRELATIONAL DISTINCTIONS 7.3