Are you referring to the residual error terms in
the model when you speak of "residuals in ANOVAs?"
In practice the observed residuals are highly
correlated and, if the design is a good one,
fluctuate in a small space with few degrees of
freedom. Applying any test for non-normality to
such observed residuals is fairly futile. Perhaps
you could clarify my confusion.
Will Hopkins wrote:
>
> We know that the residuals in ANOVAs have to be normally distributed
> if we are to believe the confidence limits or p values provided by
> the analysis, and we know that we are supposed to at least view the
> residuals for non-normality. But how much of a departure from
> non-normality does there have to be before you stop trusting the
> analysis?
>
> The Wilks-Shapiro statistic for non-normality appears to be
> equivalent to "proportion of variance in the residuals explained by
> normality", which would make it an effect statistic for normality.
> If it really is an effect statistic not biased by sample size, let's
> forget about its p value. The real question is: how small does the
> W-S have to be before things go awry with the analysis? Does anyone
> know of any simulations to answer this question, using various
> non-normal distributions? And what about using skewness and kurtosis
> in the same manner?
>
> I did a Web search first at google.com (Wilks Shapiro test
> normality). Got lots of hits, but the only thing that came close was
> some really old postings at:
> http://sobek.colorado.edu/LAB/STATS/normality.
>
> A supplementary question: Some time ago I saw someone defaulting to
> a non-parametric analysis when the sample size was small. My first
> reaction was: "that's precisely when you don't want to use
> non-parametrics, because they have less power than parametrics with
> small samples. (With large sample sizes parametrics and
> non-parametrics have the same power, for normally distributed
> residuals.)" Ah yes, but now I see that defaulting to
> non-parametrics for small sample sizes is the *safe* way to go,
> because with small samples you can't be sure the residuals in the
> population are normal, even when the residuals in the sample look
> perfectly normal. Of course, if there is no reason to suspect
> non-normality of residuals, it's reasonable to use parametrics, even
> if the residuals in the small sample look non-normal (because, you
> would reason, they look non-normal only because of sampling error).
> Comments?
>
> Will
> --
> Will G Hopkins, PhD FACSM
> University of Otago, Dunedin NZ
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Bob Wheeler --- (Reply to: [EMAIL PROTECTED])
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