[R] Levene's test

Prof Brian Ripley ripley at stats.ox.ac.uk
Fri Sep 1 11:02:58 CEST 2000

```> From: Peter Dalgaard BSA <p.dalgaard at biostat.ku.dk>
> Date: 01 Sep 2000 09:54:59 +0200
>
> Prof Brian D Ripley <ripley at stats.ox.ac.uk> writes:

Important omission: specification from Murray Jorgensen

The test that I was thinking of basically does an anova on a modified
response variable that is the absolute value of the difference between an
observation and the median of its group (more robust than Levene's original
choice, the mean).

> > 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.

This isn't really Levene's test, and I was making no claims as to validity,
just demonstrating how to do a calculation.  However, the entry
in the Encyclopedia of Statistical Sciences does say that's what done
for the original form, and appears to say the same for the Brown-Forysthe
median form, so I guess this was what Murray had in mind.

--
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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