STAT 705 -- EXAM 1 REVIEW SHEET

NOTE:  Topics A through G of part I below will not be specifically asked about on the test, 
but that material is fundamental to what follows, so you may wish to review Topics A through G.

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
    6. Mixed Models with Unbalanced Data
      a. ML estimates of model parameters
      b. Using PROC MIXED rather than PROC GLM

BLOCKING
---------

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

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


MORE LINEAR MODELS
------------------

I. Analysis of Advanced Designs

  A. Latin Square Designs
    1. When do we need a Latin Square Design?
      a. Row factor and column factor
    2. Properties of a Latin Square
    3. Advantages and disadvantages of a Latin Square
    4. Randomization Scheme for Latin Square Design
    5. Model for Latin Square
    6. ANOVA Table for Latin Square
    7. Inference (F-tests, Multiple Comparisons, etc.) and Diagnostics
    8. Latin Square designs with replication
  B. 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
 C. 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

DISTRIBUTION-FREE ALTERNATIVES IN ANOVA
---------------------------------------

I.  Kruskal-Wallis Test
  A. When is it needed?
  B. Model for Data
  C. Hypotheses for K-W Test
  D. Procedure to Calculate Ranks and Test Statistic
  E. Bonferroni Multiple Comparisons
II. Friedman Test
  A. When is it needed?
  B. Model for Data
  C. Hypotheses for Friedman Test
  D. Procedure to Calculate Ranks and Test Statistic
  E. Similar Tests and Relationships to Other Tests