Synopsis2008 - CBU statistics Wiki

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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

  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. Post-hoc tests, multiple comparisons, contrasts and handling interactions