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: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of Peter Dalgaard > Sent: Thursday, April 27, 2006 8:39 AM > To: Mike Waters > Cc: [email protected] > Subject: Re: [R] Looking for an unequal variances equivalent > of the KruskalWallis nonparametric one way ANOVA > > "Mike Waters" <[EMAIL PROTECTED]> 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 > ~~~~~~~~~~ - ([EMAIL PROTECTED]) FAX: > (+45) 35327907 > > ______________________________________________ > [email protected] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.html > ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
