# Should raw data or residuals be used to check homogeneity of variance?

Unexpectedly for me (!) I've recently learnt that:

"We have assumed that the error terms, $\epsilon_{ij}$, of the variates in each sample will be independent, that the variances of the error terms of the several samples will be equal, and, finally, that the error terms are distributed normally." [in R.R.Sokal F.J.Rohlf; Biometry, 3rd ed., 1994: p.406, section 13.4]

Does this mean that we have to operate with errors (i.e. with residuals) for checking the assumptions for statistical linear models (including repeated-measures ANOVAs) and abandon raw data?

The question is close to my previous one.

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In regression the X (design matrix part of the raw data) is non-stochastic. So, it doesn't even have a distribution. –  user603 Dec 9 '12 at 9:38
Residuals indicate how fitted values depart from the assumptions of your model, in a general sense. Their distribution matters, and has a greater interest compared to that of raw data. –  chl Dec 9 '12 at 11:35
The short answer to your question is "yes". SliLinear models make assumptions about the distribution of the errors, not the raw variable; the errors are estimated by the residuals. –  Peter Flom Dec 9 '12 at 13:34
chl and Peter Flom, thanks a lot for this clarification. Peter, what SliLinear models are? May be one of you could provide an answer? User603, sorry, but I didn't understand... –  stan Dec 9 '12 at 17:04
I believe @user603 refers to the fixed (or structural) part of the model (relationship between the response and predictors, as expressed in the design matrix) but distribution assumptions are about the random part of the model. –  chl Dec 9 '12 at 17:13

## 1 Answer

Model assumption of constancy of variance relates to the error term, not to the raw data! The residuals, in some sense, estimates the error term. So for testing model assumptions, you must use the residuals.

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