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A class of distribution-free tests for ordered alternatives in a block design is presented. On each block a distribution-free statistic is selected, and a weighted sum of these statistics is then formed. A procedure for selecting the weighting constants which maximize the asymptotic relative efficiency is presented. The improvement in the efficiency of the weighted sum of block statistics over the unweighted sum is considered and proves interesting. Some attention is also given to the idea of using different types of statistics on different blocks.
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Skillings et al. (1977) studied this question.
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