[R] Looking for an unequal variances equivalent of the Kruskal Wallis nonparametric one way ANOVA

Peter Dalgaard p.dalgaard at biostat.ku.dk
Thu Apr 27 17:38:58 CEST 2006

"Mike Waters" <michael.waters at ntlworld.com> writes:

> Well fellow R users, I throw myself on your mercy. Help me, the unworthy,
> satisfy my employer, the ungrateful. My feeble ramblings follow...
> I've searched R-Help, the R Website and done a GOOGLE without success for a
> one way ANOVA procedure to analyse data that are both non-normal in nature
> and which exhibit unequal variances and unequal sample sizes across the 4
> treatment levels. My particular concern is to be able to discrimintate
> between the 4 different treatments (as per the Tukey HSD in happier times).
> To be precise, the data exhibit negative skew and platykurtosis and I was
> unable to obtain a sensible transformation to normalise them (obviously
> trying subtracting the value from range maximum plus one in this process).
> Hence, the usual Welch variance-weighted one way ANOVA needs to be replaced
> by a nonparametric alternative, Kruskal-Wallis being ruled out for obvious
> reasons. I have read that, if the treatment with the fewest sample numbers
> has the smallest variance (true here) the parametric tests are conservative
> and safe to use, but I would like to do this 'by the book'.

What are the sample sizes like? Which assumptions are you willing to
make _under the null hypothesis_?  

If it makes sense to compare means (even if nonnormal), then a
Welch-type procedure might suffice if the DF are large.

pairwise.wilcox.test() might also be a viable alternative, with a
suitably p-adjustment. This would make sense if you believe that the
relevant null for comparison between any two treatments is that they
have identical distributions. (With only four groups, I'd be inclined
to use the Bonferroni adjustment, since it is known to be
conservative, but not badly so.)

   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907

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