Not sure that I've phrased the question correctly. If you have a series of p values from a series of tests, and they're all meant to be uniformly distributed, why do you have to do a KS test on that, and not another Chi-squared test? The following is an extract from a test program's output:- Test no. 1 p-value .886973 Test no. 2 p-value .473563 Test no. 3 p-value .358962 Test no. 4 p-value .894858 Test no. 5 p-value .767457 Test no. 6 p-value .583446 Test no. 7 p-value .227626 Test no. 8 p-value .765091 Test no. 9 p-value .298747 Test no. 10 p-value .108371 Results of the OSUM test for pu256.bin KSTEST on the above 10 p-values: .059581 The p-values are meant to be uniformly distributed across 0.0 to 1.0. This implies that they should all be 0.5ish. Why doesn't the program (Diehard randomness tester) perform a Chi-squared test on the ps? This happens several times in the complete report, so I take it to be deliberate. It's always a KS test on uniformly distributed ps. Isn't the Chi-squared test numerically simpler too?