📝 SummarXiv

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.