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

JRG loesljrg at verizon.net
Mon Dec 20 02:34:12 CET 2004

On 20 Dec 2004 at 1:11, Peter Dalgaard wrote:

> (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk> writes:
> > For non-normal data, there's something of a question as to
> > what is meant (or, perhaps more accurately, what is intended
> > to be meant) by homogeneity of variance, as a test preliminary
> > to an analysis of variance.
> 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.  They also show that the same test but with residuals taken from cell means rather than medians 
has the correct asymptotic level only if the populations are symmetric.  I don't know which version SPSS has implemented.

Carroll, R. J., & Schneider, H. (1985).  A note on Levene's tests for equality of variances.  Statistics & Probability Letters, 3, 


John R. Gleason

Syracuse University
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