[R] Homogeneity of variance tests between more than 2 sample

[Thomas Lumley]

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