Limitations of the rank transform procedure: A study of repeated measures designs, Part II

Abstract

The applicability of the transform (RT) procedure in two-way generalized repeated measures designs were each individual receives each now treatment but only one column treatment is studied. All of the common testing problems in balanced and unbalanced designs are examined. The asymptotic version of the rank transformation (Akitras, 1990) is used to identify valid RT statistics and to obtain their asymptotic properties. The two valid statistics are for the hypothesis of no row effect (H 0: all α i + γ ij = 0), and for the hypothesis of no column effect (H 0: all β j + γ ij = 0). For the hypothesis of no row effect, the error covariance matrix is allowed to depend on the column treatment but the statistic is valid only in the balanced case. It is pointed out that the validity of this statistics is due to the robustness of the F-statistic, which is also shown, to model violations incured by the rank transformation. For the hypothesis of no column effect, the statistic is shown to be valid even in the unbalanced case but the covariance matrix is assumed constant. Further, it is shown that the RT procedure is not valid for testing for main effects or for testing for interaction.