Peter, 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.
Regards, Mike -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Peter Dalgaard Sent: 27 April 2006 16:39 To: Mike Waters Cc: R-help@stat.math.ethz.ch 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 ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
