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 Analysis of Variance

## Type III Tests

The Type III Tests table is a further breakdown of the variation due to MODEL. The Sum of Squares and DF for Model are broken down into terms corresponding to the main effect for DRUG, the main effect for DISEASE, and the interaction effect for DRUG*DISEASE. The sum of squares for each term represents the variation among the means for the different levels of the factors. The Type III Tests table presents the Type III sums of squares associated with the effects in the model. The Type III sum of squares for a particular effect is the amount of variation in the response due to that effect after correcting for all other terms in the model. Type III sums of squares, therefore, do not depend on the order in which the effects are specified in the model. Refer to the chapter on "The Four Types of Estimable Functions," in the SAS/STAT User's Guide for a complete discussion of Type I -IV sums of squares.

F tests are formed from this table in the same fashion that was explained previously in the section "Analysis of Variance." In this case, there are three null hypotheses being tested: class means are all the same for the main effect DRUG, the main effect DISEASE, and the interaction effect DRUG*DISEASE. Begin by examining the test for the interaction effect since a strong interaction makes the interpretation of main effects difficult if not impossible. The computed F statistic is 1.7406 with a p-value of 0.1271. This gives little evidence for an interaction effect. Now examine the main effects. The computed F statistic for DRUG is 15.8053 with a p-value less than or equal to 0.0001. The computed F statistic for DISEASE is 4.2220 with a p-value of 0.0193. While both effects are significant, the DRUG effect appears to be stronger. Now you have more information about which means are significantly different. The results of the F test in the Analysis of Variance table indicated only that at least one of the class means is different from the others. Now you know that the difference in means can be associated with the different levels of the main effects, DRUG and DISEASE.

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