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

mike waters dr.mike at ntlworld.com
Thu Apr 27 18:41:39 CEST 2006


Thank you for your prompt response. The degrees of freedom for the 6
treatment means range from 33 to 48, so are relatively large. The Levene
test for homogeneity of variance is giving values of 13 to 14 for each of
the 5 subjective measures being analysed (i.e. highly significant for thos
d.o.f.), with skewness significant at p<0.0001 and kurtosis generally around
p<0.01 to p<0.02. I have run Bonferroni adjusted pairwise comparisons of the
means, which give approximately the same levels of significance as for the
straightforward Welch comparisons.



-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Peter Dalgaard
Sent: 27 April 2006 16:39
To: Mike Waters
Cc: R-help at stat.math.ethz.ch
Subject: Re: [R] Looking for an unequal variances equivalent of the
KruskalWallis nonparametric one way ANOVA

"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
> 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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