STAT 516 -- EXAM 2 REVIEW SHEET

I.  One-Way Analysis of Variance
 A. Basic Setup in an ANOVA
   1. What is a Factor?
   2. What are the Levels?
 B. Major Purpose of a One-Way ANOVA
   1. Main null/alternative hypotheses of interest
   2. Why analyze variances?
   3. Comparing variance AMONG sample means (between groups) 
      to variance WITHIN samples (within groups)
   4. What implies a significant difference among group means?
   5. Assumptions for ANOVA test
 C. Notation in the ANOVA setup
 D. Estimating the error variance sigma^2
   1. F-statistic is ratio of two independent estimates of sigma^2
 E. General Formulas for the elements of the ANOVA table
   1. F statistic as the ratio as MSB/MSW
   2. Partitioning the Total Sum of Squares
   3. Between-group degrees of freedom and within-group degrees of freedom
   4. How to do the Overall ANOVA F-test with the numbers in the ANOVA table
   5. Interpreting the result of the Overall ANOVA F-test
 F. Linear Model for the One-Way ANOVA
   1. "Means Model" setup
   2. "Effects Model" setup
   3.  The meaning of the "treatment effects" (the tau terms)
 G. Checking the Assumptions of the ANOVA F-test
   1. Residuals in the One-Way ANOVA
   2. Residual plots (outlier checking)
   3. Q-Q plots (checking for normality)
   4. Checking the equal-variance assumption
     a. What are the correct null & alternative hypotheses?
     b. Levene test for unequal variances
     c. How does Levene test differ from Hartley's F-max test?
     d. Remedies to stabilize unequal variances
 H. Making Specific Comparisons Among Population Means
   1. Preplanned Comparisons
   2. What is a Contrast?
   3. Choosing an appropriate contrast to answer a specific question
   4. Testing about a contrast using a t-test
 I. Post Hoc Multiple Comparisons
   1. How these are different from preplanned comparisons
   2. What exactly are we testing when we do multiple comparisons in ANOVA?
   3. Comparisonwise vs. Experimentwise error rates
   4. Fisher LSD procedure
   5. Tukey Procedure
   6. How are Fisher LSD and Tukey similar? How are they different?
 J. Random Effects Models

II. Factorial Experiments
 A. What is a factorial experiment?
   1. Main effects and Interaction effects 
 B. The Two-Factor Factorial Experiment
   1. Notation for Factors A and C and their levels
   2. The Linear Model for a Two-Factor Factorial
   3. Meaning of main effects: With interaction / without interaction
   4. Notation for the various Sample Means
 C. The (Two-Way) ANOVA table
   1. Partitioning TSS into SS(Cells) and SSW
   2. The Overall F-test for a difference in cell means
   3. Partitioning SS(Cells) into SSA, SSC, SSAC
   4. Testing for a Significant Interaction
   5. Testing for significant (main) effects of each factor
   6. Interaction plots
 D. Specific Comparisons among Factor Level Combinations
   1. Preplanned Comparisons and Contrasts
   2. How are contrasts specified when there is significant interaction?
   3. Interpreting t-tests about contrasts
 E. Post-Hoc Multiple Comparisons
   1. What do multiple comparison procedures test for in the two-factor situation?
   2. Fisher LSD procedure and Tukey procedure
 F. Additional Considerations
   1. No replication (one observation per cell)
   2. Lack of an estimate for sigma^2
   3. How does assuming no interaction help us here?
   4. Higher-order interactions with three or more factors
   5. Why might we want to assume the higher-order interaction does not exist?