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Tables of Contents for Interaction Effects in Factorial Analysis of Variance
Chapter/Section Title
Page #
Page Count
Series Editor's Introduction
v
3
Preface
viii
1. Introduction
1
32
1.1 Conceptualizations of Interaction Effects
2
18
1.1.1 Interaction Effects as the Difference Between Mean Differences
3
3
1.1.2 Interaction Effects as Treatment Effects
6
4
1.1.3 A Statistical Model for Classic Analysis of Variance
10
2
1.1.4 Factorial Designs and Mean Contrasts
12
3
1.1.5 What to Interpret: Differences Between Mean Differences or Treatment Effects/Residualized Means?
15
5
1.2 Subsidiary Analyses and Issues
20
13
1.2.1 Simple Main-Effects Analysis
20
1
1.2.2 The Choice of Error Terms
21
1
1.2.3 Graphical Representations of Interactions in 2 X 2 Designs
22
4
1.2.4 Multiple Contrasts and Experimentwise Error Rates
26
5
1.2.5 Statistical Power of Contrasts
31
2
2. Magnitude Estimation and Interval Estimation Approaches
33
23
2.1 Criticisms of Null Hypothesis Testing
33
1
2.2 Magnitude Estimation Approaches
34
11
2.2.1 Difference in Raw Means
35
1
2.2.2 Standardized Mean Difference
36
1
2.2.3 Percentage of Variance Accounted For
37
2
2.2.4 Unbiased Estimators
39
2
2.2.5 Criticisms of Indexes of Effect Size
41
4
2.3 Interval Estimation Approaches
45
11
2.3.1 Simultaneous Confidence Intervals
50
1
2.3.2 Criticisms of Interval Estimation Approaches
50
5
2.3.3 Defining a Small Confidence Interval
55
1
3. A Complete Numerical Example
56
6
4. Designs With More Than Two Levels and Higher Order Designs
62
19
4.1 A 3 X 2 Factorial Design
62
11
4.1.1 Testing the Omnibus Interaction
67
1
4.1.2 Conducting Interaction Contrasts
68
2
4.1.3 Simple Main-Effects Analysis
70
1
4.1.4 Additional Contrasts
71
1
4.1.5 Variance Partitioning
72
1
4.2 A 2 X 2 X 2 Factorial Design
73
6
4.3 Four-Factor Designs
79
1
4.4 Graphical Presentations
80
1
5. Additional Considerations
81
10
5.1 Violation of Model Assumptions
81
4
5.2 Unequal Sample Sizes
85
1
5.3 Measurement Error
86
2
5.4 Computer Analysis
88
1
5.5 Concluding Comments
89
2
Appendix: Parameter Estimates in the General Linear Model
91
4
Notes
95
2
References
97
6
About the Author
103