Question

While conducting an ANOVA test, how do you identify a list of possible contrasts and comparisons?

Answer 1

In ANOVA, comparison is defined as the weighted average of means where the weights can be negative also. Contrasts are those comparisons in which the sum of weight comes out to be zero.Thus, contrast is linear combination of variables whose sum of coefficients comes out to be zero. For example we have three treatments applied in a study and average responses for each treatment comes out to be A1,A2,A3. Then first we will check whether there is any significant effect of treatments. If it comes out, then we will see which combination of treatment gives out maximum effect. Say,we want to compare the effect of A1 with A2and A3.Thus, on camparing A1 with A2, we can use coefficient as 1,-1,0. Such that sum of coefficient =1-1+0=0, this is contrast.

So in order to list comparison and contrast, we can check the sum of coefficients if it comes out zero then only its contrast.

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