The Simultaneous Assessment of Normality and Homoscedasticity in One-Way Random Effects Models

Abstract

The article investigates the simultaneous assessment of normality and homoscedasticity in a one-way random effects model. Test procedures are developed assuming a smooth alternative to the normal distribution, specified using Legendre polynomials and Hermite polynomials. Score statistics are derived under both classes of alternatives, and a data driven approach is used to determine the order of the polynomials. Numerical results are reported in order to assess the accuracy of the chisquare distribution as the null distribution of the score statistics. Estimated powers are reported in order to compare the score tests derived under the alternatives based on Legendre polynomials and Hermite polynomials. An example and the corresponding data analysis are reported in order to illustrate the results. Possible extensions to other models involving random effects are briefly indicated.