STAT 705 -- Spring 2021 Test 2 Review Sheet

I.  Two-Factor ANOVA Models (continued)
  A. 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
    6. Mixed Models with Unbalanced Data
      a. ML estimates of model parameters
      b. Using PROC MIXED rather than PROC GLM

BLOCKING
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I. 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)
  F. Generalized Random Block Design


MORE LINEAR MODELS
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I. Analysis of Advanced Designs

  A. Repeated Measures Designs
    1. When is this appropriate?
    2. Role of subjects in the model
    3. Assumptions about variances and covariances for Y-values
      a. "Compound symmetry" assumption
      b. How can we check this?
      c. Modeling other covariance structures with PROC MIXED
    4. Analysis (ANOVA table, F-tests)
    5. Two-Factor experiments with repeated measures on one of the factors
 B. Analysis of Covariance
    1. In what situation is the ANCOVA approach used?
    2. Role of the Covariate in the ANCOVA model
      a. Principles for Choosing the Covariate
      b. "Symbolic Scatter Plot"
      c. Why / why not use ANCOVA instead of blocks?
    3. Single-Factor ANCOVA model
      a. Meaning of the (differences between) Treatment Effects
      b. F-test for significant treatment effects
      c. Test for significant covariate effect
    4. Diagnostic Plots
    5. Testing for Unequal Slopes in the ANCOVA model
      a. Role of Interaction Terms

II. 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
  E. Further Analysis of Treatment Means
  F. Meaning of "Partially Nested" designs