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Goodness and lack of fit tests to pretest normality when comparing means

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  • Pablo Flores
  • María de Lourdes Palacios

Abstract

Previous studies show that processes related to traditional pretests to prove the perfect fulfillment of assumptions in comparison means tests lead to severe alterations in the overall Type I error probability and power. These problems seem to be overcome when pretests based on an equivalence approach are used. The paper proposes a lack of fit tests based on equivalence to pretest normality on homoscedastic samples with measurable departures from normality. The Type I error probability and power produced by this equivalence pretest are compared with two traditional goodness of fit pretests and with the direct use of the t-Student and Wilcoxon test of means comparison. Furthermore, since the irrelevance limit for the lack of fit test is an arbitrary value, we propose a non-subjective methodology to find it. Results show that this proposed equivalence test controls the overall Type I Error Probability and produces adequate power; therefore, its use is recommended.

Suggested Citation

  • Pablo Flores & María de Lourdes Palacios, 2024. "Goodness and lack of fit tests to pretest normality when comparing means," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(1), pages 119-129.
    • Handle: RePEc:wut:journl:v:34:y:2024:i:1:p:119-129:id:6
    DOI: 10.37190/ord240106
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    References listed on IDEAS

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    1. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
    2. Dieter Rasch & Klaus Kubinger & Karl Moder, 2011. "The two-sample t test: pre-testing its assumptions does not pay off," Statistical Papers, Springer, vol. 52(1), pages 219-231, February.
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