Limitations of the Rank Transform Procedure: A Study of Repeated Measures Designs, Part I

Abstract

The applicability of the rank transform procedure to two-way repeated measures designs with equicorrelated errors is examined. All of the common testing problems with these models are examined. It is demonstrated that, with the exception of one testing problem, the rank transform procedure is not generally applicable. This complements the findings in Akritas (1990) for models with independent errors. The one valid rank transform statistic presented here does have the interesting feature that it allows the covariance of the equicorrelated errors to depend on the column treatment. This is due to the robustness of the corresponding F statistic to this kind of departure from the assumption of a common covariance matrix. It is shown, however, that the efficacy of this rank transform procedure has the undesirable property of depending on the model parameters.

Key Words:

• Asymptotic power
• Empirical processes
• Equicorrelated errors
• F tests