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March, 1974 Comparing Rank Tests for Ordered Alternatives in Randomized Blocks
Walter R. Pirie
Ann. Statist. 2(2): 374-382 (March, 1974). DOI: 10.1214/aos/1176342673


Two classes of rank tests are considered for ordered alternatives in a randomized block design with $k$ treatments and $n$ blocks: tests based on among-blocks rankings ($A$-tests) and tests based on within-blocks rankings ($W$-tests). Previous efficiency comparisons for fixed $k, n \rightarrow \infty$ under the normal distribution have indicated that $A$-tests are more sensitive. In the present paper it is shown that this behavior is not typical under other distributions. Further, analysis of efficiencies for fixed $n, k \rightarrow \infty$ indicates greater sensitivity for $W$-tests. Considering these results and certain other desirable properties of the $W$-tests, the latter are recommended for most applications.


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Walter R. Pirie. "Comparing Rank Tests for Ordered Alternatives in Randomized Blocks." Ann. Statist. 2 (2) 374 - 382, March, 1974.


Published: March, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0298.62012
MathSciNet: MR362696
Digital Object Identifier: 10.1214/aos/1176342673

Keywords: 15 , 62 , 70 , asymptotic efficiency comparisons , ordered alternatives , randomized blocks , rank tests

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 2 • March, 1974
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