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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

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