STAT 701 FINAL EXAM REVIEW SHEET

(The final exam will be ROUGHLY 70% new material and 30% from Exam 1 
and Exam 2 material.  Also study the review sheets for Exams 1 and 2.)

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 and "Factor-effects" formulation
    2. Interpretations of main effects and interaction effects
    3. Fitted Values and Residuals in Two-Factor ANOVA model
  D. ANOVA table
    1. Sums of Squares, degrees of freedom and Mean Squares 
    2. F-test for interaction
    3. 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
    3. Empty Cells in Two-factor studies
  I. 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. Definition of Intraclass Correlation Coefficient (ICC)
      e. CIs for overall mean, for sigma^2, for sigma_mu^2, and for ICC
    3. Two-Factor Random Effects Model 
    4. Two-Factor Mixed Model
      a. Definition of a mixed model
      b. Expected Mean Squares and how they determine correct test statistics
      c. Difference between fixed-effect hypothesis and random-effect hypothesis

II. Randomized Complete Block Design
  A. Reasoning behind Blocking
    1. Purpose of having Blocks
    2. Effect on the Model of Having Blocks
  B. Model for RCBD
    1. Differences between "random blocks" and "fixed blocks"
    2. ANOVA table for RCBD
    3. Treatment-by-Block Interaction measured as "Error"
    4. Random assignment of treatments within each block
  C. Model diagnostics in RCBD
  D. F-tests for treatment effects and block effects
  E. Further Analysis of Treatment Effects
    1. Contrasts and Multiple Comparisons
    2. Inference about ICC (if blocks random)

III. Balanced Incomplete Block Designs
  A. When must we use a BIBD?
    1. What makes it BALANCED?
    2. What makes it INCOMPLETE?
  B. Advantages and disadvantages of BIBDs
  C. Analysis and F-tests (using PROC MIXED)

IV. Latin Square Designs
  A. When do we need a Latin Square Design?
    1. Row factor and column factor
  B. Properties of a Latin Square
  C. Advantages and disadvantages of a Latin Square
  D. Randomization Scheme for Latin Square Design
  E. Model for Latin Square
  F. ANOVA Table for Latin Square
  G. Inference (F-tests, Multiple Comparisons, etc.) and Diagnostics

V. Analysis of Covariance
  A. In what situation is the ANCOVA approach used?
  B. Relationship for Regression Models with a 
     Continuous Predictor and an Indicator Predictor
    1. Measuring Change in Intercept across levels
    2. Measuring Change in Slope across levels
  C. Role of the Covariate in the ANCOVA model
    1. Principles for Choosing the Covariate
    2. "Symbolic Scatter Plot"
    3. Why / why not use ANCOVA instead of blocks?
  D. Single-Factor ANCOVA model
    1. Meaning of the (differences between) Treatment Effects
    2. F-test for significant treatment effects
    3. Test for significant covariate effect
  E. Diagnostic Plots
  F. Testing for Unequal Slopes in the ANCOVA model
    1. Role of Interaction Term

VI. Nested Designs
  A. Meaning of Nested Factors (as opposed to Crossed Factors)
  B. Notation and Model for Nested Design
  C. ANOVA table for Nested Design
    1. F-tests for Factor A and for Factor B(A)
    2. Partition of SSB(A) into components
  D. Diagnostic Plots