Actually, I've never really dealt with contrasts. I'm interested in any explanation. Granted, I could just do my own web search. I'm lazy. And I know what orthogonality is. And I know what contrasts, are. What's an orthogonal contrast? Got an example? When it is appropriate?
A contrast is just a linear combination of the model parameters where the coefficients of the combination sum to 0. A set of orthogonal contrasts is just a set of contrasts where each pair of contrasts in the set is orthogonal to one another. This is nice because we get some nice properties. In particular orthogonal contrasts are uncorrelated with one another and if we're assuming normality in our model this means that the tests of the contrasts are independent of one another. For example in a balanced 2-way anova the test of main effects and the interaction form a set of orthogonal contrasts.
One of the problems with orthogonal contrasts is that the some of the hypotheses considered may be useless because you're forcing the vectors to be indepenent of each other.
For example, consider a balanced One-Way ANOVA with 6 groups. One could easily construct 2^(6-1) -1 = 31 sets of orthogonal contrasts (without duplication) to exhaust the all of the Sums of Squares Between these groups. They certainly have the nice properties of orthogonality --- but many of these hypotheses may be completely uninterpretable.
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