# [R] Homogeneity of variance tests between more than 2 samples (long)

Landini Massimiliano numero.primo at tele2.it
Sun Dec 19 20:46:46 CET 2004

```Dear all
a couple of months ago i've found threads regard test that verify AnOVa
assumption on homogeneity of variances.  Prof. Ripley advice LDA / QDA
procedures, many books (and many proprietary programs) advice Hartley's F_max,
Cochran's minimum/maximum variance ratio (only balanced experiments), K^2
Bartlett's test, Levene's test.

Morton B. Brown and  Alan B. Forsythe in a 1974 article wrote about "Robust test
for the equality of variances" (editet by Journal of the American Statistical
Association Vol. 69, pp.: 364-367) "...the common F-ratio and BartlettÂ’s test
are very sensitive to the assumption that the underlying populations are from a
Gaussian distribution. When the underlying distributions are nonnormal, these
tests can have an actual size several times larger than their nominal level of
significance...."

Peter Armitage in  Statistical Methods in Medical Research ( Blackwell
Scientific Publication, 1971, page. 212) "...Bartlett's test maybe is less
useful than it seems; motif are two: first F test is very sensitive to the
nonnormality; second, in samples with few data, true variances must differ in
considerable manner before there is a wise/reasonable probability to obtain
results significant. In other word, even if M/C ratio is NOT significant,
estimated  variances and true variances can differ in substantial manner. If
eventually differences in true variances had weight in further analysis, is more
clever admit differences, even if tests give a non significant result..."

So, I'm asking at gurus which is best behaviour, which test they use or teach.

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Landini dr. Massimiliano
Tel. mob. (+39) 347 140 11 94
Tel./Fax. (+39) 051 762 196
e-mail: numero (dot) primo (at) tele2 (dot) it
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