[R] Levene's test

Kurt Hornik Kurt.Hornik at ci.tuwien.ac.at
Fri Sep 1 13:35:16 CEST 2000

>>>>> Peter Dalgaard BSA writes:

> Prof Brian D Ripley <ripley at stats.ox.ac.uk> writes:
>> Levene <- function(y, group)
>> {
>> group <- as.factor(group)  # precautionary
>> meds <- tapply(y, group, median)
>> resp <- abs(y - meds[group])
>> anova(lm(resp ~ group))[1, 4:5]
>> }
>> > data(warpbreaks)
>> > attach(warpbreaks)
>> > Levene(breaks, tension)
>> F value  Pr(>F)
>> group   2.818 0.06905
>> I could (and probably would) dress it up with a formula interface,
>> but that would obscure the simplicity of the calculation.

> Cough. Is that really the calculation of the P value in Levene's test?
> Just close your eyes an pretend that F is F distributed? Not that I
> don't believe that it might be the case, I just sort of expected that
> something more elaborate was required.

> I've been wondering whether we should have L's test, if for no other
> reason then because SPSS uses it by default. 

> Hmm. So we have a test (Bartlett's) which is known to be optimal under
> Normal theory, then SPSS goes and replaces with a test which uses an
> arbitrary quantity, known to be suboptimal in the Normal case, and
> tests a hypothesis that isn't actually what it purports to be
> (identical variances does not follow from identical mean absolute
> residuals), and to top it off uses a certainly incorrect calculation
> of its p-value. Well, yes they would, wouldn't they?

Btw, we have fligner.test() in ctest.  From the docs,

  The Fligner-Killeen (median) test has been determined in a simulation
  study as one of the many tests for homogeneity of variances which is
  most robust against departures from normality, see Conover, Johnson &
  Johnson (1981).


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