Andy Liaw wrote: > The long(er) answer: think harder about what question(s) you want answered > (i.e., what hypotheses you really want to test, and test only those). The > model hierarchy says that a model should not have an interaction term > involving a factor whose main effect is not present in the model. Seen in > this light, the hypothesis you're trying to test involves a non-sensical > model.
Not really. The hypothesis being tested by Type III sums of square may be suspected of not being of ``central interest'', but it is NOT (as is commonly believed) ``non-sensical''. Let us think about the 2-way ANOVA case, where one can actually understand what is going on. Let the population ***cell means*** be mu_ij (i = 1, ..., m, j = 1, ..., n) and forget about the confusing and misleading over-parameterized model. Testing for the significance of the ``row factor'' by Type III sums of squares (with interaction in the model of course) tests H_0: mu_{1.}-bar = mu_{2.}-bar = ... = mu_{m.}-bar I.e. that the means of the population cell means, over columns, are all equal. I.e. that ``when rows are averaged over columns'' there is no row effect. This could, at least conceiveably, be of interest. Note that the average is not a weighted average, saying that all columns are equally important. If all columns are NOT equally important (e.g. if an item randomly drawn from the population is more likely to ``come from'' column 1 than from column 2 etc.) then this hypothesis is less likely to be of interest. But it isn't nonsensical. It is true, however, that most of the time when people test things using Type III sums of squares they don't understand what they are really testing. But then (said he cynically) people don't understand what the hell they are really testing in most situations, not just in the context of Type III sums of squares. cheers, Rolf Turner ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help