As expected, the Uniform distribution for P-values worked well for independent two sample t tests comparing data from a Normal distribution. It did not work well for data from a skewed distribution, where the test of significance was not valid. This lack of validity is shown by the low number of P-values less than 0.05. In Figure 2, the proportion is 3.7% rather than the 5% expected for a valid test, whereas in Figure 1, where the test is valid, it is 4.8%. It did not work well for correlated two sample t tests, either. Both of these findings confirmed my prior ideas about this method. The finding for non-Normal data is particularly relevant to the idea that a reviewer could look at tests comparing mean age between randomised groups over several studies. Age seldom follows a Normal distribution in any sample of people.
