Two-Way ANOVA: Comparing Means with Two Factor Effects, Study notes of Statistics

Download Two-Way ANOVA: Comparing Means with Two Factor Effects and more Study notes Statistics in PDF only on Docsity! Two-Way ANOVA 1 Two-Way ANOVA (2 levels for each) with No Inter- action The main goal in two-way ANOVA is to compare the mean of a certain response variable across different levels of two factor effects. Taught BSE No Yes HISTORY No Ȳ00 Ȳ01 Yes Ȳ10 Ȳ11 The Model that we would like to fit is: Yi = B0 + B1HISTi + B2BSEi + i (1) Where our variables for the ith individual: Yi = Perceived benefit of mammography. And Ȳij = the average perceived benefit of mam- mography for history i and BSE j. Historyi = { 0, No History 1, History BSEi = { 0, Not Taught BSE 1, Taught BSE What does our model look like when Disease = 0? What does our model look like when Disease = 1? What does our B0 estimate? What does our B1 estimate? What does our B2 estimate? What is the overall F-test testing in terms of our means? What will the individual H0 : Bi = 0 test in terms of our means? When is it appropriate to use dummy coding, contrast coding, unweighted effect coding, and weighted effect coding? 1 2 Two-Way ANOVA Full Model w/ Dummy Coding Above we assumed that there was no interaction in the different effects. However as we saw in our first example that might not be a good assumption. Lets try refitting that model with an interaction term. We will be fitting the model: PBi = B0 + B1HISTi + B2BSEi + B3HISTi ∗BSEi i (2) Using Dummy coding what will our: What does our B0 estimate? What does our B1 estimate? What does our B2 estimate? What does our B3 estimate? What will the individual H0 : B3 = 0 test? Lets try this in SAS: proc means; by HIST BSE; VAR PB; PROC GLM DATA=MAMMO; MODEL PB = HIST BSE HIST*BSE/SOLUTION; OUTPUT OUT=OUT1 R=RY P=PY; PROC PLOT DATA=OUT1; PLOT RY*PY; RUN; QUIT; Since our interaction term is insignificant I would refit this model as an additive model (no interaction) and interpret the means separately. How could we use the Type I and Type III sums of squares, for testing the significance of two different research factors A (with four groups), B (with three groups) and A × B? When would be the appropriate time to use Type I? Type III? 2