Estudio de la afectación de la Probabilidad de error tipo I para comparar medias, cuando se pre-testea el supuesto de normalidad bajo los enfoques tradicionales y de equivalencia.

Abstract

The present research aims to study the effect on the Probability of type I error for comparing means, when the assumption of normality is pre-tested under traditional and equivalence approaches. Previous research indicates that the traditional pre-testing process causes an effect on the overall probability of committing a type I error, so a new technique based on determining irrelevance limits will be developed. In this work the programming language R Studio was used to design a new iterative pretest of lack of fit called equivalence pretest for samples with different contaminations or measurable departures from normality, the contamination is performed using the Fleishman coefficients using iterative jumps of the skewness and kurtosis, considering that the contaminations must be within Cochran's criterion and thus calculating the optimal epsilon which is used to calculate the TIEP of the equivalence test. The simulation consisted of applying 10000 repetitions in order to estimate the probability of type I error and the power of the Chi-Square and Equivalence pretests, as well as of the t-Student and Wilcoxon mean comparison tests. The results obtained from the study conclude that the procedures proposed are reliable for a mean comparison test for contamination levels (0-6). When comparing the traditional goodness-of-fit test and the pretest designed for lack of fit used to test normality, it is shown that pretesting under the equivalence approach controls the overall probability of type I error, and with respect to power, the equivalence pretest is better than the traditional pretest, so this approach is considered more reliable. It is recommended to use the equivalence pretest developed to test the assumption of normality, in order to reduce the effect of the overall TIEP on the mean comparison tests.