Experimental Design & Analysis for Psychology
Herve Abdi, Betty Edelman, Dominique Valentin, and W. Jay Dowling
Table of Contents
1 Introduction to Experimental Design
1.1. General overview
1.2. Independent and dependent variables
1.3. Independent variables
1.4. Dependent variables
1.5. Common defective experimental designs
1.6. The choice of subjects and the representative design of experiments
1.7. Key notions of the chapter
2 Correlation
2.1. Introduction
2.2. Correlation: Overview and Example
2.3. Rationale and computation of the coefficient of correlation
2.4. Interpreting correlation and scatterplots
2.5. The importance of scatterplots
2.6. Correlation and similarity of distributions
2.7. Correlation and Z-scores
2.8. Correlation and causality
2.9. Squared correlation as common variance
2.10. Key notions of the chapter
2.11. Key formulas of the chapter
2.12. Key questions of the chapter
3 Statistical Test: The F test
3.1. Introduction
3.2. Statistical Test
3.3. For experts: Not zero is not enough!
3.4. Key notions of the chapter
3.5. New notations
3.6. Key formulas of the chapter
3.7. Key questions of the chapter
4 Simple Linear Regression
4.1. Generalities
4.2. The regression line is the "best-fit" line
4.3. Example: Reaction Time and Memory Set
4.4. How to evaluate the quality of prediction
4.5. Partitioning the total sum of squares
4.6. Mathematical Digressions
4.7. Key notions of the chapter
4.8. New notations
4.9. Key formulas of the chapter
4.10. Key questions of the chapter
5 Orthogonal Multiple Regression
5.1. Generalities
5.2. The regression plane is the "best-fit" plane
5.3. Back to the example: Retroactive interference
5.4. How to evaluate the quality of the prediction
5.6. F tests for the simple coefficients of correlation
5.7. Partitioning the sums of squares
5.8. Mathematical Digressions
5.9. Key notions of the chapter
5.10. New notations
5.11. Key formulas of the chapter
5.12. Key questions of the chapter
6 Non-Orthogonal Multiple Regression
6.1. Generalities
6.2. An example: Age, speech rate and memory span
6.3. Computation of the regression plane
6.4. How to evaluate the quality of the prediction
6.5. Semi-partial correlation as increment in explanation
6.5. F tests for the semi-partial correlation coefficients
6.6. What to do with more than two independent variables
6.7. Bonus: Partial correlation
6.8. Key notions of the chapter
6.9. New notations
6.10. Key formulas of the chapter
6.11. Key questions of the chapter
7 ANOVA One Factor: Intuitive Approach
7.1. Introduction
7.2. Intuitive approach
7.3. Computation of the F ratio
7.4. A bit of computation: Mental Imagery
7.5. Key notions of the chapter
7.6. New notations
7.7. Key formulas of the chapter
7.8. Key questions of the chapter
8 One Factor, S(A): Test, Computation, & Effect Size
8.1. Statistical test: A refresher
8.2. An example: back to mental imagery
8.3. Another more general notation: A and S(A)
8.4. Presentation of the results of the ANOVA
8.5. ANOVA with two groups: F and t
8.6. Another example: Romeo and Juliet
8.7. How to estimate the effect size
8.8. Computational formulas
8.9. Key notions of the chapter
8.10. New notations
8.11. Key formulas of the chapter
8.12. Key questions of the chapter
9 One Factor, S(A): Regression Point of View
9.1. Introduction
9.2. Example 1: Memory and Imagery
9.3. Analysis of variance for Example 1
9.4. Regression approach for Example 1: Mental Imagery
9.5. Equivalence between regression and analysis of variance
9.6. Example 2: Romeo and Juliet
9.7. f regression and analysis of variance are one thing, why keep two different techniques?
9.8. Digression
9.9. Multiple regression and analysis of variance
9.10. Key notions of the chapter
9.11. Key formulas of the chapter
9.12. Key questions of the chapter
10 Design: S(A): Score Model
10.1. The score model
10.2. ANOVA with one random factor (Model II)
10.3. The Score Model: Model II
10.4. F 1 or The Strawberry Basket!
10.5. Three exercises
10.6. Key notions of the chapter
10.7. New notations
10.8. Key formulas of the chapter
10.9. Key questions of the chapter
11 The Assumptions of Analysis of Variance
11.1. Overview
11.2. Validity assumptions
11.3. Testing the Homogeneity of variance assumption
11.4. Example
11.5. Testing Normality: Lilliefors
11.6. Notation
11.7. Numerical example
11.8. Numerical approximation
11.9. Transforming scores
11.10. Key notions of the chapter
11.11. New notations
11.12. Key formulas of the chapter
11.13. Key questions of the chapter
12 Planned Orthogonal Comparisons
12.1. General overview
12.2. What is a contrast?
12.3. The different meanings of alpha
12.4. An example: Context and Memory
12.5. Checking the independence of two contrasts
12.6. Computing the sum of squares for a contrast
12.7. An other view: Contrast analysis as regression
12.8. Critical values for the statistical index
12.9. Back to the Context
12.10. Significance of F vs. specific contrasts
12.11. How to present the results of orthogonal comparisons?
12.12. The omnibus F is a mean
12.13. Sum of orthogonal contrasts: Subdesign analysis
12.14. Key notions of the chapter
12.15. New notations
12.16. Key formulas of the chapter
12.17. Key questions of the chapter
13 Planned Non-orthogonal Comparisons
13.1. General Overview
13.2. The classical approach
13.3. Multiple regression: The return!
13.4. Key notions of the chapter
13.5. New notations
13.6. Key formulas of the chapter
13.7. Key questions of the chapter
14 Post hoc or a-posteriori analyses
14.1. Introduction
14.2. Scheff ´e's test: All possible contrasts
14.3. Pairwise comparisons
14.4. Key notions of the chapter
14.5. New notations
14.6. Key questions of the chapter
15 Two Factors, S(A × B)
15.1. Introduction
15.2. Organization of a two-factor design: A × B
15.3. Main effects and interaction
15.4. Partitioning the experimental sum of squares
15.5. Degrees of freedom and mean squares
15.6. The Score Model (Model I) and the sums of squares
15.7. An example: Cute Cued Recall
15.8. Score Model II: A and B random factors
15.9. ANOVA A × B (Model III): one factor fixed, one factor random
15.10. Index of effect size
15.11. Statistical assumptions and conditions of validity
15.12. Computational formulas
15.13. Relationship between the sources
5.14. Key notions of the chapter
15.15. New notations
15.16. Key formulas of the chapter
15.17. Key questions of the chapter
16 Factorial designs and contrasts
16.1. Introduction
16.2. Fine grained partition of the standard decomposition
16.3. Contrast and standard decomposition
16.4. What error term should be used?
16.5. Example: partitioning the standard decomposition
16.6. Contrasts non-orthogonal to the canonical decomposition
16.7. A posteriori Comparisons
17 One Factor Repeated Measures design, S × A
17.1. Introduction
17.2. Examination of the F Ratio
17.3. Partitioning the SSwithin: S(A) = S + SA
17.4. Computing F in an S × A design
17.5. A numerical example: S × A design
17.6. Score Model: Model I and II for repeated measures designs
17.7. Estimating the size of the experimental effect
17.8. Problems with repeated measures
17.9. An example with computational formulas
17.10. Another example: Proactive interference
17.11. Score model (Model I) S × A design: A fixed
17.12. Score model (Model II) S × A design: A random
17.13. Key notions of the chapter
17.14. New notations
17.15. Key formulas of the chapter
17.16. Key questions of the chapter
18 Two Factors Completely Repeated Measures: S × A × B
18.1. Introduction
18.2. An example: Plungin'!
18.3. Sum of Squares, Means squares and F ratios
18.4. Score model (Model I), S × A × B design: A and B fixed
18.5. Results of the experiment: Plungin'
18.6. Score Model (Model II): S × A × B design, A and B random
18.7. Score Model (Model III): S × A × B design, A fixed, B random
18.8. Quasi-F: F'
18.9. A cousin F''
18.10. Validity assumptions, measures of intensity, key notions, etc
18.11. New notations
18.12. Key formulas of the chapter
19 Two Factors Partially Repeated Measures: S(A) × B
19.1. Introduction
19.2. An Example: Bat and Hat
19.3. Sums of Squares, Mean Squares, and F ratio
19.4. The comprehension formula routine
19.5. The 13 points computational routine
19.6. Score model (Model I), S(A) × B design: A and B fixed
19.7. Score model (Model II), S(A) × B design: A and B random
19.8. Score model (Model III), S(A) × B design: A fixed and B random
19.9. Coefficients of Intensity
19.10. Validity of S(A) × B designs
19.11. Prescription
19.12. New notations
19.13. Key formulas of the chapter
19.14. Key questions of the chapter
20 Nested Factorial Designs: S × A(B)
20.1. Introduction
20.2. An Example: Faces in Space
20.3. How to analyze an S × A(B) design?
20.4. Back to the example: Faces in Space
20.5. What to do with A fixed and B fixed
20.6. When A and B are random factors
20.7. When A is fixed and B is random
20.8. New notations
20.9. Key formulas of the chapter
20.10. Key questions of the chapter
21 How to derive expected values for any design
21.1. Crossing and nesting refresher
21.2. Finding the sources of variation
21.3. Writing the score model
21.4. Degrees of freedom and sums of squares
21.5. An example
21.6. Expected values
21.7. Two additional exercises
A Descriptive Statistics
B The sum sign: P
C Expected Values
D Elementary Probability: A Refresher
E Probability Distributions
F The Binomial Test
G Statistical tables