An approximate test of variance homogeneity based on grubbs' estimators

Abstract

Consider a two-way, n x r, classification or a randomized block design with n treatments and r blocks. The usual model is modified so that error components have variances for the j‐th column or block. Let Q_j: be Grubbs1 estimator of An approximate test of the hypothesis is proposed and based on the statistic, −½(n−1)(r−1)(n−2) log T_r, where , which is taken to have the central chi-square distribution with (r−1) degrees of freedom. Simulation studies for r=3(1)6(2)12 and n=10, 20, 30, 50 confirm that the approximate distribution is satisfactory for applications.

Keywords:

• block variances
• moment approximations
• simulation
• approximate test
• chi-square distribution