Re: Formal test for pooled variance?

On Fri, 30 Dec 2005 12:17:49 GMT, "Shiquiliq" <shiquiliq@xxxxxxxxx>
wrote:

> Ok, so what I'm hearing is that, in general, I should assume
> heteroskedasticity (unequal variances), unless there is some structural
> reason to assume equal variances.

A "structural reason" is a pretty good reason to assume
equal variances. But there can be "structural reasons"
for the variances to increase with the means, which
happens when the data should have been measured
as (say) logarithms, or tested as square root (Poisson).

If the variances are equalized by a rational transformation,
that's a pretty good reason to transform. "Non-parametric
tests" from ranks are another alternative. Some people
argue that the rank-order transformation preserves so
much of the power, even when the data are normal,
that it is always a safe alternative -- But the rank test
does assume that the distributions are the same form
or shape or family.

"Assuming heteroskedasticity" by using that t-test with
separate variance estimates also makes it harder to
make direct comparison to other analyses that may be
in the same report.

Hope that helps.

--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.

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