Abstract
Abstract To test for treatment effects in a two-way model when the classical assumptions of normality of errors and constancy of variance cannot be verified, Hora and Conover (1984) proposed a rank test in which the entire data set is ranked, the ranks are scored, and then the classical analysis of variance F statistic is applied to the scored ranks. They showed that the limiting null distribution of this test statistic is a chi-squared distribution divided by its degrees of freedom. Simulation results suggest that this procedure, called the rank-transform procedure, has good power properties. This article determines the asymptotic relative efficiency of the rank-transform procedure relative to the classical F statistic. To do this, vectors of linear rank statistics are shown to have a limiting multivariate normal distribution under a sequence of Pitman alternatives. This work is based on the results of Hajek (1968). The rank-transform statistic is then expressed as a quadratic form in the vectors, divide...
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