I considered Fisher’s exact test one-sided. This is also testing a null hypothesis which is known to be true. This might be expected again to lead to a Uniform distribution. However, here the one-sided test Fisher’s exact test as implemented in Stata 12 sums all probabilities smaller than that for the table observed for tables in the direction away from the expected frequencies. The direction is not specified in advance, so the resulting P-values are never much greater than 0.5. It is not a true one-sided test. Here the largest P-value was 0.513.
