Synopsis of the Graduate Statistics Course 2007

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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