Pretesting strategies for homoscedasticity when comparing means. Their robustness facing non-normality

Abstract

Traditional pretests to prove homoscedasticity (e.g., Levene’s or Bartlett’s test) before applying normal parametric techniques like the Student’s t test should be avoided: Given the form of their null and alternative hypotheses, they are methodologically inadequate to this end and induce overall (regarding the full testing process, pretesting included) alterations in Type I Error Probability (TIEP). Under normality, not pretesting and always applying the Welch’s test (instead of Student’s test) or pretesting with the Wellek’s equivalence test of heteroscedasticity irrelevance, are more affordable strategies. Here we investigate the robustness, in front of non-normality, of five strategies dealing with possible heteroscedasticity: Pretesting with Levene, F and Wellek’s, and applying either the Student’s or the Welch’s test directly without pretest. Non-normality is simulated by varying degrees of skewness and kurtosis, for distributions inside the Fleishman’s system. Robustness is measured in terms of overall TIEP proximity to the nominal significance level. The direct use of Welch’s test or pretesting with the Wellek’s test are still the most robust approaches, although high degrees of contamination of normality affect them considerably. All approaches improve with growing sample sizes and worsen with unbalancing, but differences still persist, in general favoring the above mentioned two approaches.

KEYWORDS:

• Equivalence test
• Heteroscedasticity irrelevance
• Assumptions