[R] Homogeneity of variance tests between more than 2 sample
Thomas Lumley
tlumley at u.washington.edu
Mon Dec 20 16:41:37 CET 2004
On Sun, 19 Dec 2004, JRG wrote:
> On 20 Dec 2004 at 1:11, Peter Dalgaard wrote:
>>> Yes... If you use the test as a preliminary to an ANOVA, which largely
>> depends on second order properties, I think it is reasonable to assume
>> that you really mean to compare the variances. It's always been a
>> mystery to me why SPSS prefers the Levene test, which tests whether
>> the mean absolute deviation is identical, which is a pretty obviously
>> not the same thing, unless you assume something like the distributions
>> being scaled versions of eachother.
>
> I don't use SPSS, but "Levene's test" is often taken to mean "an ANOVA
> on absolute deviations from cell medians". Carroll & Schneider (1985)
> show that such a test has the correct asymptotic level, and that it
> works pretty well as a test of equality of scale for non-normal
> distributions.
Yes, but that is the level under the strong null of equality of
distributions, not under the null hypothesis that variances are equal (for
possibly non-equal distributions). Peter's point (and perhaps Ted's
earlier point) is that the equal mean absolute deviation from the median
is not the same as equal variance so a test can't possibly be valid for
both.
-thomas
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