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 varianceFstatistic 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 classicalFstatistic. 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 Hájek (1968). The rank-transform statistic is then expressed as a quadratic form in the vectors, divided by a consistent estimator of a variance component. It is then shown that the limiting distribution of this statistic is a noncentral chi-squared distribution divided by its degrees of freedom. The efficacy of the rank-transform procedure is the noncentrality parameter of this chi-squared distribution, which is shown to be close to the efficacy of the Kruskal—Wallis test. For the special case in which the data can be represented as a one-way layout, this efficacy coincides with the Kruskal—Wallis efficacy.