Power of <i>t</i>-test for Simple Linear Regression Model with Non-normal Error Distribution: A Quantile Function Distribution Approach

Abstract

One of the major assumptions of the regression analysis is the normality assumption of the model error. We generally assume that the error term of the simple linear regression model is normally distributed. But in this paper g-and-k distribution is used as the underlying assumption for the distribution of error in simple linear regression model and a numerical study is conducted to see what extent of the deviation from normality causes what extent of effect on the size and power of t-test for simple linear regression model with the deviation being measured by a set a of skewness and kurtosis parameters. The strength of t-test is evaluated by observing the power function of t-test. The simulation result shows that, the performance of the t-test for simple linear regression model with g-and-k error distribution is seen to be vastly affected in presence of excess kurtosis and small samples (i.e. n<100).t-test is size robust under normal situation. Skewness and kurtosis parameter has a very little effect on the size of the t-test.

© 2012 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.

doi: http://dx.doi.org/10.3329/jsr.v4i3.9067 J. Sci. Res. 4 (3), 609-622(2012)