Pretesting Assumptions for the validity of two sample Mean Tests

Abstract:

The Student’s t-test [12] to prove possible inequalities of two population means is subject to normality and homoscedasticity assumptions which traditionally are verified through pretests. This strategy is sometimes recommended in statistical books and courses. When in a normality pretest (Shapiro Wilk, Kolmogorov Smirnov, Anderson darling, etc.) the null hypothesis of perfect normality is rejected, a non-parametric test (Wilcoxon-Mann-Whitney test) is usually used ([15],[6])-sometimes wrongly assuming its robustness in front of heteroscedasticity. Otherwise, normality is assumed and a parametric procedure like the t-test or the Welch’s test [13] is used. Which of these procedures is chosen depends on an additional pretest to compare variances (F, Levene, Bartlet...). If the null hypothesis of perfect variances equality is not rejected, homoscedasticity is assumed and the t-test is used, otherwise the final decision is based on the Welch’s test. There are several studies ([5],[8],[11],[16],[10]) showing that pretesting alters the overall Type I Error Probability (TIEP). These authors agree in advising against pretesting, and sometimes recommending the direct use (without pretest) of the Welch’s test as the standard option, since it keeps the overall TIEP stable around the nominal significance level α.

Año de publicación:

2018

Keywords:

Fuente:

google