A Comparison of Two Rank-Based Methods for the Analysis of Linear Models

Two rank-based methods for analyzing linear models are compared. A robust general linear model (RGLM); similar to least squares, offers a complete analysis of a model, including estimation, testing, and diagnostic checks. It is supported by asymptotic theory and is highly efficient. The other is the rank transform (RT), which offers a testing procedure. Unlike RGLM, the RT is not supported by a general theory, and although initial simulation studies appeared promising, recent theoretical and Monte Carlo studies question the wisdom of doing RT's on designs as simple as two-way models. The two analyses are contrasted over factorial designs on which they can substantially differ. These differences are highlighted in a simulation study on a three-way factorial design. We conclude the contrast with an analysis of covariance example.