I have data from an experiment in which five different methods were used to abrade a ceramic and the resulting particle size in the atmosphere measured. Due to the anisotropic nature of the ceramic there is considerable scatter in the data which is right skewed, and robvar shows the data to fail the homogeneity of variance test.
Array

I used a log transform
Array
There is still inhomogeneity in the variance but the distribution of residuals following anova appears to be normal as assessed visually using distplot (from SSC)
. robvar lc, by(method)

| Summary of lc
method | Mean Std. Dev. Freq.
------------+------------------------------------
1 | -4.5900172 .18631618 900
2 | -2.2221745 1.2543433 1,800
3 | -2.2856141 .74755 1,800
4 | -2.6684095 .90676613 900
5 | -3.2487493 .35297332 900
------------+------------------------------------
Total | -2.7889648 1.1870132 6,300

W0 = 572.11260 df(4, 6295) Pr > F = 0

W50 = 528.26727 df(4, 6295) Pr > F = 0

W10 = 552.20502 df(4, 6295) Pr > F = 0

My question is it acceptable to use this log transformed data; or would another transformation be preferable; or should I consider a nonparametric analysis such as dunntest (from SSC).

Thank you.
Eddy