ANOVA Procedures for Multiple Linear Regression Model with Non-normal Error Distribution: A Quantile Function Distribution Approach

摘要

This paper is an attempt to observe the extent of effect on the power of analysis of variance test to violations of assumptions i.e. normality assumption of the error of multiple linear regression model. The error of the model is considered as g- and-k distribution because of the fact that it has shown a considerable ability to fit to data and facility to use in simulation studies. The strength of ANOVA is evaluated by observing the power function of F- test for different combination of g (skewness) and k (kurtosis) parameter. From the simulation results it is observed that the performance of ANOVA is seen to be immensely affected in presence of excess kurtosis and for small samples (say, n <100). Skewness parameter has not much effect on the power of the test under non-normal situation. The effect of sample size on the existing test for multiple regression models is also observed here in this paper under various non normal situations.