STAT 704 Test 3 Review Sheet I. Regression Models with Qualitative Predictors A. Role of Indicator Variables B. Calculations/Interpretions of Mean Response C. Qualitative Predictors with Several Categories 1. Effects of Different Ways of Specifying Indicators II. Single-Factor ANOVA Model A. Difference between Regression Models and ANOVA models 1. Factors (how they differ from predictors in regression) a. Qualitative and Quantitative Factors b. Advantages/Disadvantages of ANOVA model compared to Regression 2. Levels of a Factor 3. Experimental Units, Observational Units, Subjects B. ANOVA Model Assumptions C. Cell-Means Model and Notation 1. Relationship to "general linear model" form 2. Least Squares estimation of Parameters in One-Way ANOVA model 3. Fitted Values and Residuals in the ANOVA Model D. Analysis of Variance for a Single-Factor Study 1. SSTO, SSTR, SSE a. What type of variability does each SS measure? b. Variability AMONG treatment means vs. variability WITHIN treatments 2. Degrees of Freedom for each SS 3. MSTR and MSE and their expected values 4. ANOVA F-test for Equality of Factor Level Means a. Null and alternative hypotheses b. Test statistic value c. Distribution of test statistic under H_0 d. What does the F-test result help you to conclude? 5. Factor Effects Model and alternate formulation of F-test H_0 E. Regression Approach to ANOVA model 1. General Linear Model form of Factor Effects Model 2. Interpretation of the model parameters in terms of the mean response 3. Role of Indicator Variables 4. Fitting Cell-Means Model through Regression F. Power calculation for F-test 1. Definition of power of a hypothesis test 2. Relationship of F-test power to sample sizes 3. Relationship of F-test power to spread of true level means 4. Relationship of F-test power to within-level variance 5. Using Table B.12 III. Further Investigation in One-Way ANOVA E. Investigation of Differences Among Treatment Means 1. When do we investigate the treatment means further? 2. Simple plots (bar graph, main effects plot) 3. Inference about an Individual Population Treatment Mean a. CI for an Individual Population Treatment Mean b. t-test about an Individual Population Treatment Mean 4. Inference about a PAIR of Population Treatment Means a. CI for the Difference between Two Population Treatment Means b. t-test Comparing Two Population Treatment Means F. Contrasts 1. Formal Definition of a Contrast 2. How a Contrast can help us compare various Population Treatment Means 3. CI and t-test about a contrast G. Simultaneous Inference 1. Why we must account for simultaneous inferences a. Data snooping b. Family significance level, family confidence level 2. Tukey's Multiple Comparison Procedure a. Simultaneous CIs for ALL Pairwise Differences between Two Population Treatment Means b. Simultaneous Tests comparing ALL Pairs of Population Treatment Means 3. Other Multiple Comparison Procedures a. Scheffe method and Bonferroni method b. When are these methods preferred? H. Checking Model Assumptions in ANOVA 1. Residual Plot (vs. Fitted Values) 2. Normal Q-Q plot of residuals 3. Testing Equal-Variance Assumption Using Brown-Forsythe Test 4. Testing Normality Assumption using Shapiro-Wilk Test 5. Possible Remedies for Violation(s)