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. 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

4. 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

5. 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

6. 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