Alternativas para o teste t com variâncias heterogêneas avaliadas por meio de simulação

Abstract

This work aimed to measure the type I and II error rates with the increases of the difference among populational variances through computational simulation using Student t test with degrees of freedom proposed by Satterthwaite (1946), or degrees of freedom given by υ = min (n1 - 1, n2 - 1) and an alternative given by bootstrap method. Two populations were generated. The variance of the first population was considered equal to 1, and the variance of the population 2 was specified in function of the ratio σ22/σ21, which assumes the values of 1, 2, 8 and 16. Using these three different approaches the type I and II error rates were evaluated. All the approaches controlled appropriately the type I error rates; the Student t with degrees of freedom given by υ = min (n1 - 1, n2 - 1) was more rigorous than the other approaches when the samples had different sizes. This approach presented larger type II error rates than the others to the situations of great variance heterogeneity. The bootstrap procedure better controlled the type II error rates to situations of different sample sizes (n1=5 and n2=30, n1=10 and n2=30) and of variances ratios larger than 1.