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

[Mike Waters]

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'.

TVMIA,

Regards,

Mike