A numerical investigation of the accuracy of parametric bootstrap for discrete data

For simple discrete models, parametric bootstrap tests can be calculated explicitly rather than simulated. Moreover, their accuracy can also be calculated exactly as a function of the nuisance parameter. This article reports the results of an intensive numerical investigation of the accuracy of first order and parametric bootstrap based tests, firstly of treatment effect in clinical trials, and secondly of association in simple logistic regression. We conclude that bootstrap tests have asymptotic size error that decreases at rate O(m−1) but that their excellent small sample performance has little to do with asymptotics.