Heteroscedasticity irrelevance when testing means difference

• Pablo Flores M. ^[2] ; Jordi Ocaña ^[1]
  1. [1] Universitat de Barcelona

     Universitat de Barcelona

     Barcelona, España

     
  2. [2] Escuela Superior Politécnica de Chimborazo
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 42, Nº. 1, 2018, págs. 59-72
• Idioma: inglés
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• Resumen

  • Heteroscedasticity produces a lack of type I error control in Student’s t test for difference between means. Pretesting for it (e.g., by means of Levene’s test) should be avoided as this also induces type I error. These pretests are inadequate for their objective: not rejecting the null hypotheses is not a proof of homoscedasticity; and rejecting it may simply suggest an irrelevant heteroscedasticity. We propose a method to establish irrelevance limits for the ratio of variances. In conjunction with a test for dispersion equivalence, this appears to be a more affordable pretesting strategy.