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Consider testing the hypothesis of no treatment effects against a postulated ranking of the treatments, given data from n complete blocks. A suitable test statistic is the weighted average rank correlation W = where Ci correlation between the postulated ranking and the ranking observed within the i-th block, Qi is the rank of the i-th block with respect to credibility, and the b's are weights such that 0<=b1<=...<=bn. Tests using Spearman and Kendall correlation are proposed and their distributions are obtained for both small and large experiments. These tests and others are compared in small experiments with respect to expected significance level. Finally, a simple illustrative example is presented.
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Salama et al. (1981) studied this question.
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