STAT 705 -- EXAM 2 REVIEW SHEET

I.  Two-Factor ANOVA
  A. Definition of Treatments as Factor Level Combinations
  B. Weaknesses of the "One Factor at a Time" Approach
  C. Notation for the Two-Factor ANOVA model
    1. Cell-means formulation
    2. X matrix and "beta vector" for the formulation
    3. "Factor-effects" formulation
    4. Interpretations of main effects and interaction effects
    5. Fitted Values and Residuals in Two-Factor ANOVA model
  D. ANOVA table
    1. Sums of Squares, degrees of freedom, Mean Squares and Expected Mean Squares
    2. Checking model assumptions
    3. Interaction plots and their interpretations
    4. F-test for interaction
    5. F-tests for main effects (When appropriate?)
  E. Further Investigation of Factor Effects (No Interaction)
    1. CI for a factor level mean
    2. CI and test about contrast of factor level means
    3. Pairwise Multiple Comparisons of Factor Level Means
  F. Further Investigation of Factor Effects (With Interaction)
    1. CIs and tests about individual cell means
  G. One-observation-per-treatment Situation
    1. Problem estimating sigma^2
    2. Assumption of No Interaction
    3. "Tukey test of Additivity"
  H. Unbalanced Data Situation
    1. Reasons for Unequal Sample Sizes
    2. Type III SS and LSMEANS statement in SAS
      a. Regression approach (Full/reduced) to analyze factor effects
      b. Definition of "least squares mean"
    3. Empty Cells in Two-factor studies

II.  More Complicated ANOVA Models
  A. Three or More Factors
    1. Several different types of interaction terms in model
    2. Role of high-order interactions
  B. Random and Mixed Effects Models
    1. How do we decide whther to treat levels as fixed or random?
    2. Cell Means Model for One Factor with random levels
      a. Normal distribution for random effects
      b. Variance of random effects
      c. Correct hypothesis to test about random effects
      d. Assumptions about variances and covariances for Y-values in random-effects model
      e. Definition of Intraclass Correlation Coefficient (ICC)
    3. Inference in Random Effects Model
      a. CI for overall mean
      b. CI for sigma^2
      c. CI for sigma_mu^2
      d. CI for ICC
    4. Two-Factor Random Effects Model 
    5. Two-Factor Mixed Model
      a. Definition of a mixed model
      b. Expected Mean Squares and how they determine correct test statistics
      c. Importance of correct denominator MS in F-statistic
      d. Difference between fixed-effect hypothesis and random-effect hypothesis