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

• Authors: FLORES Pablo , PALACIOS María de Lourdes
• Languages of publication: EN

Abstracts

EN

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

EN

normality; lack of fit; goodness of fit; equivalence; assumptions; Type I error probability

• Publisher: Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
• Journal: Operations Research and Decisions
• Year: 2024
• Volume: 34
• Issue: 1
• Pages: 119-129

Contributors

author

FLORES Pablo

• Grupo de Investigación en Ciencia de Datos CIDED, Facultad de Ciencias, Escuela Superior Politécnica de Chimborazo (ESPOCH), Riobamba, Ecuador

author

PALACIOS María de Lourdes

• Carrera de Matemáticas, Facultad de Ciencias, Escuela Superior Politécnica de Chimborazo (ESPOCH), Riobamba, Ecuador

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Identifiers

DOI

10.37190/ord240106