Issue: 2024/Vol.34/No.1, Pages 119-129
GOODNESS AND LACK OF FIT TESTS TO PRETEST NORMALITY WHEN COMPARING MEANS
Pablo Flores
, María de Lourdes Palacios
Cite as: P. Flores, M. d. L. Palacios. Goodness and lack of fit tests to pretest normality when comparing means. Operations Research and Decisions 2024: 34(1), 119-129. DOI 10.37190/ord240106
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.
Keywords: normality, lack of fit, goodness of fit, equivalence, assumptions, type I error probability
Received: 19 March 2023 Accepted: 12 January 2024
Published online: 28 March 2024