R. L. Anderson proposed a $\chi^2$-type rank statistic for the nonparametric analysis of a randomized blocks design. In this paper the asymptotic distribution of the test statistic is derived under a sequence of alternatives contiguous to the null hypothesis. Using Bahadur's concept of local approximate slope, it is shown that the test is optimal within a large class of rank tests including the tests proposed by Friedman and by Page. The results are extended to BIB designs. Ties are considered.
"An Alternative to the Friedman Test with Certain Optimality Properties." Ann. Statist. 7 (3) 537 - 550, May, 1979. https://doi.org/10.1214/aos/1176344675