## 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**