Afectación de las pruebas de comparación de medias ante alteraciones de la homocedasticidad

Abstract

In this work, whose objective was to estimate the TIEP (Type I Error) and the Power generated by the mean comparison tests when there are homoscedasticity comparison tests of means when there are alterations of homoscedasticity in different sample sizes, an algorithm was created to estimate the TIEP and the Power of the parametric tests (t-Student, t-Welch, ANOVA of a single factor, Welch’s ANOVA) which is based on Monte Carlo simulation, the samples were established according to this research interest such as balanced samples, unbalanced ascending samples, unbalanced ascending samples (t-Student, t-Welch, ANOVA of a single factor, Welch’s ANOVA) and unbalanced ascending samples (t-Student, t-Welch, Welch’s ANOVA), unbalanced ascending (small samples corresponding to small variances and large samples to large variances) and unbalanced descending (small samples corresponding to large variances and large samples to small variances) 2, 3 and 5 means, in order to reach the research’s main objective, different contaminations established for the variance ratio were performed, giving as a result that when homoscedasticity exists the parametric tests t-Student, the t- Welch and the ANOVA test of a single factor, are more efficient in all samples respectively, although the power is relatively lower, especially in small sample sizes, whether balanced or unbalanced, with the exception of the Welch’s ANOVA test, which is not efficient in all samples and when homoscedasticity is altered, the parametric tests t-Student and ANOVA of a single factor are very sensitive (or not robust) to deviations from homoscedasticity and their power is relatively lower, especially in small sample sizes, whether balanced or unbalanced, and as for t-Welch and Welch’s ANOVA, they are efficient in most cases in medium-large and large balanced samples.