The Curriculum

The content of the sequence of stat courses follows. Even in my own notes, I call this list below the “aspirational sequence,” and I have (largely) tried to order it so that the more I can get through it with a given cohort is not only the extent to which I’ve covered what I hope a Ph.D. sequence could, but the extent to which I was able to teach efficiently at that time.

The Aspiring Sequence

  1. Descriptive Statistics
    1. Levels of Measurement
    2. Central Tendency
    3. Variance & Covariance
    4. Presenting Data
  2. Introduction to Probability
    1. Odds Ratios
    2. Contingency Tables
      1. Fisher’s Exact Test
  3. Introduction to Distributions
    1. Normal Distribution
    2. Normal Approximations of Distributions
    3. t & χ² Distributions
  4. Applications of Distributions
    1. Confidence Intervals
    2. Standardization
      1. z Scores
      2. Effect Size
      3. Correlations
  5. Populations & Samples
    1. Standard Error of the Mean & Regression to the Mean
    2. Power & Sample Size Estimation
  6. Hypothesis Testing
    1. Null Hypothesis
    2. Type I & II Errors
    3. χ² Tests
  7. t Tests
    1. Paired t test
    2. Two-Sample t Test (Equal & Unequal Samples)
  8. Introduction to Linear Regressions
    1. Method of Ordinary Least Squares
    2. Model Assumptions
  9. Introduction to ANOVAs
    1. Main Effects & Interactions
    2. Reading Source Tables
    3. R²
  10. ANOVAs continued
    1. Family-Wise Error, Post hoc, & Planned Comparisons
  11. The ANOVA “Family” of Models: ANCOVAs, MANOVAs, & repeated-Measures ANOVAs
  12. Longitudinal Analyses
    1. Pre–Post Differences
    2. (Repeated-Measures) ANCOVAs with Pretest as Covariate
    3. Multilevel Models of Change
  13. Tests of Model Fit
    1. Latent Constructs
    2. Information Criteria
    3. Stepwise Analysis
  14. Introduction to Structural Equation Modelling
  15. Foundations of Measurement and Scaling
    1. The Origins of Science
  16. Validity
    1. Traditional, Trinity View
    2. The 1999–2014 Standards & Validity as “Use”
  17. Reliability
    1. Classical Measurement Theory View
    2. As a Measure of a Unitary Construct
    3. As a Measure of Internal Consistency
      1. Cronbach’s α
      2. Kuder-Richardson Formulae 20 & 21
    4. Other Forms (Test-Retest, etc.)
  18. Items as Measurements of Factors
    1. History1 of Psychometrics
    2. Latent Variables
  19. Factor Analysis
    1. Concept and Basic Ideas (shared variance, total shared variance & model fits, etc.)
    2. Eigenvalues
    3. Exploratory Factor Analysis
      1. Uses and abuses
    4. Confirmatory Factor Analysis
      1. Measures of Model Fit
  20. Return to Structural Equation Modelling

  1. Mercifully brief and germane.↩︎