# Compare means - heterogeneous variance, non-normal

I would like to perform some basic means comparisons (3 conditions, balanced, n = 21 for a total of 63 observations). The main dependent variable is total task completion time, i.e., the experimental question of interest is: Does task completion time differ across the 3 experimental conditions?

The data are non-normal and the variances are not homogeneous across the groups (smallest variance is about 10 times the largest). Due to the large difference in variance, I understand that a non-parametric alternative (like Kruskal-Wallis) would likely be inappropriate. A log transformation of task completion time does improve the situation--normalizes the residuals in 2 of the 3 conditions and results in homogeneous variances.

My main question is: Is a log transformation justified here? If so, could I still use ANOVA after the transformation, even though 1 of the conditions is still non-normal?

• To be honest, I'd probably fit a GLM for this, possibly with a gamma or perhaps inverse-gaussian distribution family, depending on the skewness and the way the variance relates to the mean. The null hypothesis you have there would be simple enough in that framework. You could do a permutation test, or there are still other alternatives. – Glen_b -Reinstate Monica Sep 12 '13 at 1:37