Alteración de la probabilidad global de error tipo I en las pruebas de comparación de dos medias cuando se verifican sus supuestos.

Abstract

The objective of this study was to estimate the global probability of committing a Type I error of the tests to compare equality of two measures (t-Student, Welch and Wilcoxon), when their assumptions of normality and homoscedasticity are pre-tested. Previous research shows that the traditional pre-testing process produces serious alterations in the Type I Error Probability, and it is recommended to eliminate this process from the traditional teaching of statistics. Later studies show that the problem is not to pre-test the assumptions, but the way they are posed. An equivalency approach to pre-test could eliminate the problems described. In this work, stochastic simulation algorithms were developed to estimate the Type I Error Probability when the two assumptions are pre-tested together, for samples with different contaminations or departures from normality and homoscedasticity. The generation of non-normal samples was made from the Fleishman contamination system, which allowed the generation of samples of unknown distribution and with a distance of measurable normality. The level of heteroscedasticity is established from the ratio between the population variances that generate the samples. The results show that pre-testing under the traditional approach significantly alters the overall probability in Error Type I, especially for small samples and Pre-testing under the equivalence approach, seems to better control this probability of error, that is why this approach is considered more reliable than the traditional one, and it is even striking that, for samples with unknown distributions, this technique is more robust than the Wilcoxon test, which supposedly is designed exclusively for this type of samples. Finally, some possible future research on the subject is discussed.