On the power of robust tests in analysis of covariance

Abstract

The simple analysis of covariance model is considered where the response variable is modeled in terms of one classification variable (with two groups) and one independent variable or covariate. The usual tests of parallelism and equality of adjusted means for this model are evaluated for a number of different testing procedures. The power of the standard t test procedures, based on the least squares estimates, are compared for small samples by Monte Carlo techniques to the power of proposed t-like and F-like tests procedures based on M estimates. These procedures are compared across a variety of error distributions which include the normal and contaminated normals. The results show that the power of the t-like procedures are highly robust in that they maintain near equal power to the usual t tests under normal errors while resulting in greater power, sometimes substantially greater, than the usual t tests when the errors are from the contaminated normal family. The F-like tests cannot be recommended because their power curves never exceed those for the usual t tests or the t-like tests.

Keywords:

• M estimator
• iterated reweighted least squares
• t-like tests
• F-like tests
• test for adjusted means
• test for parallelism
• general linear model