A Non-Parametric Test for a Two-Way Analysis of Variance

Stefano Bonnini, Michela Borghesi, Gianfranco Piscopo () and Massimiliano Giacalone
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Stefano Bonnini: Department of Economics and Management, University of Ferrara, Via Voltapaletto 11, 44121 Ferrara, Italy
Michela Borghesi: Department of Economics and Management, University of Ferrara, Via Voltapaletto 11, 44121 Ferrara, Italy
Gianfranco Piscopo: Department of Mathematics and Applications “Renato Caccioppoli”, University of Naples “Federico II”, Via Cintia, Monte S. Angelo, 80126 Napoli, Italy
Massimiliano Giacalone: Capua (CE)—Department of Economy, University of Campania “Luigi Vanvitelli”, Corso Gran Priorato di Malta, 81043 Capua, Italy

Mathematics, 2025, vol. 13, issue 7, 1-17

Abstract: The methodology carried out in this work is based on non-parametric inference. The problem is framed as a regression analysis, and the solution is derived using the permutation approach. The proposed test does not rely on the assumption that the distribution of the response follows a specific family of probability laws, unlike other parametric approaches. This makes the test powerful, particularly when the typical assumptions of parametric approaches, such as the normality of data, are not satisfied and parametric tests are not reliable. Furthermore, this method is more flexible and robust with respect to parametric tests. A permutation test on the goodness-of-fit of a multiple regression model is applied. Hence, proposed solution consists of the application of permutation tests on the significance of the single coefficients and then a combined permutation test (CPT) to solve the overall goodness-of-fit testing problem. Furthermore, a Monte Carlo simulation study was performed to evaluate the power of the previously mentioned permutation approach, comparing it with the conventional parametric F -test for ANOVA and the bootstrap combined test, both commonly discussed in the literature on this statistical problem. Finally, the proposed non-parametric test was applied to real-world data to investigate the impact of age and smoking habits on medical insurance costs in the USA. The findings suggest that smoking and being at least 50 years old significantly contribute to increased medical insurance costs.

Keywords: non-parametric inference; permutation tests; ANOVA (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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