More surprising was the lack of fit to the Uniform distribution found for P-values for chi-squared tests based on a large sample. These tests should be valid, because the expected frequencies are close to 500, far greater than the 5.0 required by the usual criterion. The proportion with P<0.05 is 5.6%, close to the 5% expected for a valid test when all null hypotheses are true. I found the graininess and unevenness of the distribution of P-values for chi-squared tests, even with a very large sample, quite surprising.
