Synopsis of the CBU Graduate Statistics Course 2008

  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