Nonparametric Analysis of Balanced Incomplete Block Rank Data

Abstract

Traditional nonparametric analysis of balanced incomplete block rank data usually involves the Durbin test. Here we give an alternative adjustment for the Durbin statistic for when there are ties and mid-ranks are used. The adjusted Durbin statistic is shown to be simply related to the ANOVA F statistic on the ranks, so that the corresponding tests are, in a sense, equivalent. This means both are tests of equality of mean treatment ranks. A simulation study compares the size and power performances of the competing tests. We also apply the nonparametric ANOVA methodology to give tests for univariate moment effects and, when treatments are ordered, for bivariate moment effects. The latter includes umbrella tests.