Why not a Permutation Test?
A permutation test would avoid the problem of assuming normality. The idea is to limit the number of assumptions on the data-generating mechanism and approximate a sampling distribution by permuting — or relabeling — observations. In this case, choosing a null distribution from which to resample is problematic. The two natural choices are (1) randomly dividing all teams into groups of 16 and (2) randomly assigning one of each seed to each region. The assumption of complete randomness is unrealistic because the committee would never allow Duke, Connecticut, Villanova, Texas and Kansas to play in the same region. On the other hand, randomly assigning one of each seed to each region assumes that the committee was able to perfectly seed each team — an assumption which is clearly wrong. (Indeed, by checking for imbalance in the brackets, we are implicitly checking for seeding errors which caused it.) Can’t we Compare the Seeds Historically? Historical comparisons are possible, but are no
