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