Comparison of the robustness of alternatives to the two sample test under non normality distributions through Monte Carlo simulation

Abstract

This work aimed to evaluate the risks of committing type I and type II errors in non normal populations by means of computational simulation and to compare three tests usually applied. It was compared the t test with the approach of the degrees of freedom proposed by Satterthwaite (1946), t with the degrees of freedom given by v = min (n₁ - 1, n₂ - 1) and bootstrap method under different distributions of probability. Under non normal distribution the t with Satterthwaite adjustment of degrees of freedom and with v = min (n₁ - 1, n₂ - 1) degrees of freedom did not control type I error probabilities. The bootstrap criterion controlled the type I error rates and presented equivalent power being considered robust with the violation of the normality assumption. The t test under non normal distribution with Satterthwaite adjustment of degrees of freedom with samples of different sizes presented type I error rates greater than the nominal levels.