Been stuck on this problem for a few days. I have calculated many distributions that are all non-parametric, but appear to have trended to be approximately normal. I think a helpful way to visualize what I've done is a matrix with 24 columns and 16 rows. Each cell has one of these distributions. I have test statistics for which I know the row(one from each row), but not the column that they came from. I also know the probability of picking each of the columns (this is constant across all test statistics, but the probabilities of picking each column are not equal). Is there some way to show significance across an entire row? All of these distributions have n=1000, but have very different means. It's obvious that an ANOVA F test with the null hypothesis that all means are equal would be highly significant.