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The Anatomy of Statistics: Models, Hypotheses, Significance and Power Experiments, Data, Models and Parameters Probability vs. Statistics Hypotheses and Inference The Likelihood Function Estimation and Inferences Maximum Likelihood Estimate (MLE) Schools of Statistical Inference Ronald Aylmer FISHER Jergy NEYMAN and Egon PEARSON Rev. Thomas BAYES R A Fisher: P values and Significance Tests Neyman and Pearson: Hypothesis Tests Type I & Type II Errors Size and Power Exploratory Data Analysis (EDA) What is it? Skew and kurtosis: definitions and magnitude rules of thumb Pictorial representations - in particular histograms, boxplots and stem and leaf displays Effect of outliers Power transformations Rank transformations Categorical Data Analysis The Naming of Parts Categorical Data Frequency Tables The Chi-Squared Goodness-of-Fit Test The Chi-squared Distribution The Binomial Test The Chi-squared test for association Simpson, Cohen and McNemar SPSS procedures that help Frequencies Crosstabs Chi-square Binomial Types of Data Quantitative Qualitative Nominal Ordinal Frequency Table Bar chart Cross-classification or Contingency Table Simple use of SPSS Crosstabs Goodness of Fit Chi-squared Test Chance performance and the Binomial Test Confidence Intervals for Binomial Proportions Pearson’s Chi-squared Yates’ Continuity Correction Fisher’s Exact Test Odds and Odds Ratios Log Odds and Log Odds ratios Sensitivity and Specificity Signal Detection Theory Simpson’s Paradox Measures of agreement: Cohen's Kappa Measures of change: McNemar’s Test Association or Independence: Chi-squared test of association Comparing two or more classified samples Regression What is it? Expressing correlations (simple regression) in vector form Scatterplots Assumptions in regression Restriction of range of a correlation Comparing pairs of correlations Multiple regression Least squares Residual plots Stepwise methods Synergy Collinearity Between subjects analysis of variance What is it used for? Main effects Interactions Simple effects Plotting effects Implementation in SPSS Effect size Model specification Latin squares Balance Venn diagram depiction of sources of variation The General Linear Model and complex designs including Analysis of Covariance GLM and Simple Linear Regression The Design Matrix Least Squares ANOVA and GLM Types of Sums of Squares Multiple Regression as GLM Multiple Regression as a sequence of GLMs in SPSS The two Groups t-test as a GLM One-way ANOVA as GLM Multi-factor Model Additive (no interaction) Non-additive (interaction) Analysis of Covariance Simple regression 1 intercept 1 slope Parallel regressions multiple intercepts 1 slope Non-parallel regressions multiple intercepts multiple slopes Sequences of GLMs in ANCOVA Power analysis Hypothesis testing Boosting power Effect sizes: definitions, magnitudes Power evaluation methods:description and implementation using an examples nomogram power calculators SPSS macros spreadsheets power curves tables quick formula Repeated Measures and Mixed Model ANOVA Two sample t-Test vs. Paired t-Test Repeated Measures as an extension of paired measures Single factor Within-Subject design Sphericity Two (or more) factors Within-Subject design Mixed designs combining Within- and Between-Subject factors Mixed Models, e.g. both Subjects & Items as Random Effects factors The ‘Language as Fixed Effects’ Controversy Testing for Normality Single degree of freedom approach Latent variable modelling – factor analysis and all that! Path diagrams – a regression example Comparing correlations Exploratory factor analysis Assumptions of factor analysis Reliability testing (Cronbach’s alpha) Fit criteria in exploratory factor analysis Rotations Interpreting factor loadings Confirmatory factor models Fit criteria in confirmatory factor analysis Equivalence of correlated and uncorrelated models Cross validation as a means of assessing fit for different models Parsimony : determining the most important items in a factor analysis What to do following an ANOVA Why do we use follow-up tests? Different ways to follow up an ANOVA Planned vs. Post Hoc Tests Choosing and Coding Contrasts Handling Interactions Standard Errors of Differences Multiple t-tests Post Hoc Tests Trend Analysis Unpacking interactions Multiple Comparisons: Watch your Error Rate! Post-Hoc vs A Priori Hypotheses Comparisons and Contrasts Family-wise (FW) error rate Experimentwise error rate Orthogonal Contrasts or Comparisons Planned Comparisons vs. Post Hoc Comparisons Orthogonal Contrasts/Comparisons Planned Comparisons or Contrasts Contrasts in GLM Post Hoc Tests Control of False Discovery Rate (FDR) Simple Main Effects