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?