Introduction and summary
It is now coming to be generally agreed that in testing for shift in the two-sample problem, certain tests based on ranks have considerable advantage over the classical t-test. From the beginning, rank tests were recognized to have one important advantage: their significance levels are exact under the sole assumption that the samples are randomly drawn (or that the assignment of treatments to subjects is performed at random), whereas the t-test in effect is exact only when we are dealing with random samples from normal distributions. On the other hand, it was felt that this advantage had to be balanced against the various optimum properties possessed by the t-test under the assumption of normality. It is now being recognized that these optimum properties are somewhat illusory and that, under realistic assumptions about extreme observations or gross errors, the t-test in practice may well be less efficient than such rank tests as the Wilcoxon or normal scores test [6], [7].
Received JaDuary 30, 1960.
This paper was prepared with the partial support of the Office of Naval Research (nonr- 222-43) . This paper in whole or in part may be reproduced for any purpose of the United States Government.
And for the case of paired comparisons, which also turns out to lend itself particularly well to a rank analysis
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Keywords
- Null Distribution
- Balance Incomplete Block Design
- Asymptotic Efficiency
- Null Variance
- Restricted Randomization
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References
Benard, A. and Elteren, Ph. van (1953). A generalization of the method of m-rank-ings. Indag. Math. 15 358–369.
Durbin, J. (1951).Incomplete blocks in ranking experiments. British J. Psych. 4 85–90.
Elteren, Ph. van (1960); On the combination of independent two sample tests of Wil-coxon. Bull. Inst. Internat. Statist. 37 351–361.
Elteren, Ph. van and Noether, G. E. (1959). The asymptotic efficiency of the κx2 n-test for a balanced incomplete block design. Biometrika 46 475–477.
Friedman, M. (1937). The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J. Amer. Statist. Assoc. 32 675–698.
Hodges, J. L., Jr. and Lehmann, E. L. (1956). The efficiency of some non-parametric competitors of the t-test. Ann. Math. Statist. 27 324–335.
Hodges, J. L., Jr. and Lehmann, E. L. (1961). Comparison of the normal scores and Wilcoxon tests. Proc. Fourth Berkeley Symp. Math. Statist. Prob. 1 307–317. Univ. of California Press.
Loève, M. (I960). Probability Theory, 2nd ed. Van Nostrand, Princeton.
Walsh, John E. (1959). Exact nonparametric tests for randomized blocks. Ann. Math. Statist. 30 1034–1040.
Wilcoxon, F. (1946). Individual comparisons of grouped data by ranking methods. J. of Entomology 39 269–270.
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Hodges, J.L., Lehmann, E.L. (2012). Rank Methods for Combination of Independent Experiments in Analysis of Variance. In: Rojo, J. (eds) Selected Works of E. L. Lehmann. Selected Works in Probability and Statistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1412-4_35
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