An Alternative to the Friedman Test with Certain Optimality Properties

Abstract

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.