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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.

Simple vs. Complex Interactions • An interaction is considered simple if we can discuss trends for the main effect of one factor for each level of the other factor, and if the general trend is the same. • An interaction is complex if it is difficult to discuss anything about the main effects. In this situation, one can only look at

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