Abstract
For each of the N-values 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1,024, 50,000 samples of size N were drawn from an L-shaped population, and for each sample the Z and t statistics were calculated. The resulting distributions of 50,000 Z or t values at each sample size were then used to study the robustness of left-tailed, right-tailed, and two-tailed Z and t tests at α levels of.05,.01, and.001 (and, for Z only,.0001). The actually obtained proportion, ρ, of Type I errors was often far greater or far smaller than the nominal proportion, α. Furthermore, although α is the expected value of ρ at infinite N, no N-value below 512 ever brought the deviation of p from α to within 10% of α for any t tests or one-tailed Z tests.