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

[Berton Gunter]

Why not bootstrap or simulate (e.g. permutation test)? Sounds like exactly
the sort of situation for which it's designed.

-- Bert
 

> -----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: Thursday, April 27, 2006 8:39 AM
> 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 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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