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The Asymptotic Distributions of Statistics arising in Certain Non-Parametric Tests

Published online by Cambridge University Press:  18 May 2009

Samuel D. Silvey
Samuel D. Silvey
Affiliation:
University of Glasgow
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In a previous paper [5] the equivalence of randomisation and normal theory distributions of linear combinations was discussed. In the present paper we discuss the asymptotic randomisation distributions of statistics used in analysis of variance and in a closely related problem which includes, in particular, the “problem of m-rankings“. Kruskal [4] has studied the first of these questions in the case where observations are replaced by ranks.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 2 , Issue 1 , April 1954 , pp. 47 - 51
Copyright
Copyright © Glasgow Mathematical Journal Trust 1954

References

REFERENCES

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(4)Kruskal, W. H., “A non-parametric test for the several sample problem,” Ann. Math. Stats., 23, 4 (1952.).CrossRefGoogle Scholar
(5) Silvey, S. D., “The equivalence of asymptotic distributions under randomisation and normal theories,” Proc. Glasgow Math. Ass., 1, 3 (1953).Google Scholar
(6)Wald, A., and Wolfowitz, J., “Statistical tests based on permutations of the observations,” Ann. Math. Stats., 15, 4, (1944).CrossRefGoogle Scholar