Five tests for the hypothesis of no treatment effects in complete blocks designs are compared with respect to asymptotic relative efficiency: the ordinary two-way analysis of variance, the analysis of variance of ranks (Friedman, 1937), the method of ranking after alignment (Hodges and Lehmann, 1962), and a method of weighted rankings proposed by Quade (1972, 1979). This comparison required devising a procedure for estimating the asymptotic relative efficiencies of test statistics with asymp-totic chi-squared distributions.