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 X B) 15.1. Introduction 15.2. Organization of a two-factor design: A X 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 X 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 X 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 X A design 17.5. A numerical example: S X 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 X A design: A fixed 17.12. Score model (Model II) S X 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 X A X 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 X A X B design: A and B fixed 18.5. Results of the experiment: Plungin' 18.6. Score Model (Model II): S X A X B design, A and B random 18.7. Score Model (Model III): S X A X 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) X 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) X B design: A and B fixed 19.7. Score model (Model II), S(A) X B design: A and B random 19.8. Score model (Model III), S(A) X B design: A fixed and B random 19.9. Coefficients of Intensity 19.10. Validity of S(A) X 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 X A(B) 20.1. Introduction 20.2. An Example: Faces in Space 20.3. How to analyze an S X 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