Estudio de potencia de pruebas de normalidad usando distribuciones desconocidas con distintos niveles de no normalidad.

Abstract

Most parametric tests are subject to normality. There are forty different tests to prove this assumption. Preliminary researches to determine the best tests are based on the estimation of their power using samples from known non-normal distributions but whose distance or contamination from normality is unknown. In the present study, we selected seven better and more known tests. Through a simulation process, we estimate the power of each one using samples from unknown distributions but with a measurable distance from normality. It seems that Shapiro - Wilk test is the best option, its power is very high, but only for large non-normal samples and strong distances. For distributions with weak distances and small samples it seems that none of the traditional tests are good. We discuss a possible poor approach to these tests and their impact on the results obtained. Finally, the possibility of including a hypothesis test based on the equivalence approach is analyzed; perhaps this option is better than the traditional tests introduced.