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Question: I need to know if there is a way to partial ANOVAsor Chi Squares the same way you can do with linear regression. Specifically, what I am trying to find out is, holding age of onset ofsymptoms constant (partialling it out), do blacks enter treatment fordementia with greater symptoms than whites? We have done a bunch of simple chi-squares and ANOVAs so far, but thisis a more complex question that can't be addressed with suchmethodology, as far as I know... I have a large database which we are trying to analyze and we arereally stumped here! Any help ???
Answer: So far as I know, this is the purpose of Analysis of Covariance (ANCOVAor ANACOVA). In this technique you use a sort of regression to adjust themeans of each group for the covariate (age of onset in your design)before doing the basic ANOVA computations. The covariate will probablypull some variance out of the error term and make it easier to detect theeffects of interest (race, in your design). Most serious stats packages ought to be able to handle a simple ANCOVAdesign like you seem to have. No, sorry, that is not "the purpose" of ANCOVA. If you aregoing to do ANOVA as a standard technique, then you better be assured,for your standard analyses, that there is no meaningful differencebetween groups on the covariate, and your "purpose" is the reduction ofthe error term rather than adjusting for differences. That is the SAFEuse of ANCOVA. If the groups are NOT EQUAL on the covariate, then you have to seriouslyconsider the implications... "controlling for differences" is sometimesa reasonable interpretation, but it should never be assumed without athought. In this instance, I find some good reason to wonder about oddrelationships and selection-factors in determining the samples. Dementiasymptoms increase with age; but is that true if you select for "entryinto treatment for dementia?" Since dementia is not *expected* inthe young, the differential diagnosis might require an excess ofsymptoms, compared to what would bring in an older person. I would look at an overlay-plot of the two groups, age by symptom-level,and do my wondering from there. If there should be regressions withthe same slopes for the two groups, then the ANCOVA interpretationmight be reasonable.
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