Research Information System
Statistics, 2025 (SCI-Expanded)
In this study, we propose robust tests for testing the interaction and main effects in two-way analysis of variance (ANOVA) in the presence of violations of the classical ANOVA assumptions such as normality and homogeneous variances. Specifically, we consider unbalanced heteroscedastic two-way ANOVA with long-tailed symmetric (LTS) distributed errors. LTS distribution is a plausible alternative to the normal distribution especially for modelling data sets with outliers due to its symmetric and heavy tailed nature. In developing the proposed tests, the parametric bootstrap (PB) approach by Krishnamoorthy et al. [A parametric bootstrap approach for anova with unequal variances: fixed and random models. Comput Stat Data Anal. 2007;51(12):5731–5742] is employed and the resulting tests are called as robust PB (RPB). The unknown model parameters are estimated by using modified maximum likelihood (MML) methodology since the MML estimators are robust and asymptotically equivalent to maximum likelihood estimators, see Tiku [Estimating the mean and standard deviation from a censored normal sample. Biometrika 1967;54(1–2):155–165]. To compare the performances of the proposed RPB tests with their normal theory counterparts called as PB tests, extensive Monte Carlo simulation studies are conducted, see Xu et al. [A parametric bootstrap approach for two-way anova in presence of possible interactions with unequal variances. J Multivar Anal. 2013;115:172–180] in the context of normal theory heteroscedastic two-way ANOVA. Simulation results indicate that the proposed RPB tests show better power performances than the corresponding PB tests especially for the larger kurtosis values of the LTS distribution. Also, they are remarkably robust to the deviations from the assumed model and to the data anomalies. Finally, a real data set is analysed to illustrate the practical applicability of the proposed methodology.