Beyond the traditional simulation design for evaluating type 1 error: from ‘theoretical’ to ‘empirical’ null

When evaluating a new statistical test, it’s important to check the type 1 error (T1E) control, often achieved by the `theoretical' design S0. In whole-genome association analyses, people scan through large numbers of genes (Gs) for the ones associated with an outcome(Y). Y comes from an unknown alternative and is not associated with the majority of Gs, This reality can be represented by two `empirical’ designs, where S1.1 simulates Y from G then evaluates its association with independently generated Gnew; while S1.2 evaluates the association between permutated Yperm and G. Using scale tests, location tests with single and multiple Gs as examples, we show that not all designs are equal. For certain statistics, T1E inflation can only be revealed under 1empirical’ designs and doesn’t diminish as sample size increases. This important observation calls for new practices for methods evaluation and interpretation of T1E control.M.Sc