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Lecture 27 Two-Way ANOVA: Interaction

27-1 Lecture 27 Two-Way ANOVA: Interaction STAT 512 Spring 2011 Background Reading KNNL: Chapter 19 27-2 Topic Overview Review: Two-Way ANOVA Models Basic Strategy for Analysis Studying Interactions 27-3 Two-Way ANOVA Factor Effects model ()ijki jijkijY = + + + + where ()2~ 0,ijkN are independent and ()0iiij = == SAS uses different constraints: 0a =, 0b =, and ()0ij = for i = a or j = b. 27-4 Constraints / Comparisons Under the usual constraints everything gets compared to the GRAND MEAN Under SAS constraints everything gets compared to the mean for the last level of each factor. In either case, differences are identified and contrasts can be used with the results being exactly the same. So in the big picture, you should be able to produce the basic estimates, but otherwise do not need to worry too much about the constraints. 27-5 Factor Effects (under the textbook constraints) Grand Mean: Estimate by Yiii Main Effects Estimate i by i iY Y = ii iii Estimate i by j jY Y = i i iii Interaction : Estimate ()ij by () ij ijijY Y Y Y = +i ii i i iii 27-6 General Strategy for Multiple ANOVA Analysis Every thing we are doing can be extended to any number of variables.

the model, but using marginal means for each significant main effect individually • Marginal means: Averages over the levels of the other factor. 27-10 ... • Report that the interaction is significant; plot the means and describe the pattern. • Discuss results for the levels of A for each level of B or vice versa . 27-13

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