Smooth Tests for Normality in ANOVA

Peiwen Jia, Xiaojun Song and Haoyu Wei

Papers from arXiv.org

Abstract: The normality assumption for random errors is fundamental in the analysis of variance (ANOVA) models, yet it is rarely formally tested in practice. In this paper, we propose Neyman's smooth tests for assessing the normality assumption across various types of ANOVA models. The proposed test statistics are constructed based on the Gaussian probability integral transformation of ANOVA residuals. Under the null hypothesis of normality, the test statistics are asymptotically Chi-square distributed, with degrees of freedom determined by the dimension of the smooth model (the number of orthonormal functions). A data-driven selection of the model dimension using a modified Schwarz's criterion is also discussed. Simulation studies demonstrate the effectiveness of our proposed method.

Date: 2021-10, Revised 2025-09
New Economics Papers: this item is included in nep-cwa
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2110.04849

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