Experimental Design and Analysis for Psychology
Herve Abdi, Betty Edelman, Dominique Valentin, and W. Jay Dowling
Table of Contents
1 Introduction to Experimental Design
1.1: Introduction
1.2: Independent and dependent variables
1.3: Independent variables
1.4: Dependent variables
1.5: Choice of subjects and 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: 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: Introduction
4.2: Generalities
4.3: The regression line is the "best-fit" line
4.4: Example: Reaction Time and Memory Set
4.5: How to evaluate the quality of prediction
4.6: Partitioning the total sum of squares
4.7: Mathematical Digressions
4.8: Key notions of the chapter
4.9: New notations
4.10: Key formulas of the chapter
4.11: Key questions of the chapter
5 Orthogonal Multiple Regression
5.1: Introduction
5.2: Generalities
5.3: The regression plane is the "best-fit" plane
5.4: Back to the example: Retroactive interference
5.5: 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: Introduction
6.2: 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 and Computation of F
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 ANOVA, One Factor: Test, Computation, and Effect Size
8.1: Introduction
8.2: Statistical test: A refresher
8.3: Example: back to mental imagery
8.4: Another more general notation: A and S(A)
8.5: Presentation of the ANOVA results
8.6: ANOVA with two groups: F and t
8.7: Another example: Romeo and Juliet
8.8: How to estimate the effect size
8.9: Computational formulas
8.10: Key notions of the chapter
8.11: New notations
8.12: Key formulas of the chapter
8.13: Key questions of the chapter
9 ANOVA, one factor: 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: If regression and analysis of variance are one thing, why keep two different techniques?
9.8: Digression: when predicting Y from Ma., b=1
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 ANOVE, one factor: Score Model
10.1: Introduction
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: Size effect coefficients derived from the score model: w2 and p2
10.6: Three exercises
10.7: Key notions of the chapter
10.8: New notations
10.9: Key formulas of the chapter
10.10: Key questions of the chapter
11 Assumptions of Analysis of Variance
11.1: Introduction
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 Analysis of Variance, one factor: Planned Orthogonal Comparisons
12.1: Introduction
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: Another view: Contrast analysis as regression
12.8: Critical values for the statistical index
12.9: Back to the Context
12.10: Significance of the omnibus F vs. significance of 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 ANOVA, one factor: Planned Non-orthogonal Comparisons
13.1: Introduction
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 ANOVA, one factor: Post hoc or a posteriori analyses
14.1: Introduction
14.2: Scheffe'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 More on Experimental Design: Multi-Factorial Designs
15.1: Introduction
15.2: Notation of experimental designs
15.3: Writing down experimental designs
15.4: Basic experimental designs
15.5: Control factors and factors of interest
15.6: Key notions of the chapter
15.7: Key questions of the chapter
16 ANOVA, two factors: AxB or S(AxB)
16.1: Introduction
16.2: Organization of a two-factor design: AxB
16.3: Main effects and interaction
16.4: Partitioning the experimental sum of squares
16.5: Degrees of freedom and mean squares
16.6: The Score Model (Model I) and the sums of squares
16.7: An example: Cute Cued Recall
16.8: Score Model II: A and B random factors
16.9: ANOVA AxB (Model III): one factor fixed, one factor random
16.10: Index of effect size
16.11: Statistical assumptions and conditions of validity
16.12: Computational formulas
16.13: Relationship between the names of the sources of variability, df and SS
16.14: Key notions of the chapter
16.15: New notations
16.16: Key formulas of the chapter
16.17: Key questions of the chapter
17 Factorial designs and contrasts
17.1: Introduction
17.2: Vocabulary
17.3: Fine grained partition of the standard decomposition
17.4: Contrast analysis in lieu of the standard decomposition
17.5: What error term should be used?
17.6: Example: partitioning the standard decomposition
17.7: Example: a contrtast non-orthogonal to the canonical decomposition
17.8: A posteriori Comparisons
17.9: Key notions of the chapter
17.10: Key questions of the chapter
18 ANOVA, one factor Repeated Measures design: SxA
18.1: Introduction
18.2: Advantages of repeated measurement designs
18.3: Examination of the F Ratio
18.4: Partitioning the within-group variability: S(A) = S + SA
18.5: Computing F in an SxA design
18.6: Numerical example: SxA design
18.7: Score Model: Models I and II for repeated measures designs
18.8: Effect size: R, R and R
18.9: Problems with repeated measures
18.10: Score model (Model I) SxA design: A fixed
18.11: Score model (Model II) SxA design: A random
18.12: A new assumption: sphericity (circularity)
18.13: An example with computational formulas
18.14: Another example: proactive interference
18.15: Key notions of the chapter
18.16: New notations
18.17: Key formulas of the chapter
18.18: Key questions of the chapter
19 ANOVA, Ttwo Factors Completely Repeated Measures: SxAxB
19.1: Introduction
19.2: Example: Plungin'!
19.3: Sum of Squares, Means squares and F ratios
19.4: Score model (Model I), SxAxB design: A and B fixed
19.5: Results of the experiment: Plungin'
19.6: Score Model (Model II): SxAxB design, A and B random
19.7: Score Model (Model III): SxAxB design, A fixed, B random
19.8: Quasi-F: F'
19.9: A cousin F''
19.10: Validity assumptions, measures of intensity, key notions, etc
19.11: New notations
19.12: Key formulas of the chapter
20 ANOVA Two Factor Partially Repeated Measures: S(A)xB
20.1: Introduction
20.2: Example: Bat and Hat
20.3: Sums of Squares, Mean Squares, and F ratio
20.4: The comprehension formula routine
20.5: The 13 point computational routine
20.6: Score model (Model I), S(A)xB design: A and B fixed
20.7: Score model (Model II), S(A)xB design: A and B random
20.8: Score model (Model III), S(A)xB design: A fixed and B random
20.9: Coefficients of Intensity
20.10: Validity of S(A)xB designs
20.11: Prescription
20.12: New notations
20.13: Key formulas of the chapter
20.14: Key questions of the chapter
21 ANOVA, Nested Factorial Designs: SxA(B)
21.1: Introduction
21.2: Example: Faces in Space
21.3: How to analyze an SxA(B) design
21.4: Back to the example: Faces in Space
21.5: What to do with A fixed and B fixed
21.6: When A and B are random factors
21.7: When A is fixed and B is random
21.8: New notations
21.9: Key formulas of the chapter
21.10: Key questions of the chapter
22 How to derive expected values for any design
22.1: Introduction
22.2: Crossing and nesting refresher
22.3: Finding the sources of variation
22.4: Writing the score model
22.5: Degrees of freedom and sums of squares
22.6: Example
22.7: Expected values
22.8: Two additional exercises
A Descriptive Statistics
B The sum sign: E
C Elementary Probability: A Refresher
D Probability Distributions
E The Binomial Test
F Expected Values
Statistical tables