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Non-Parametric Inference for Ordered Alternatives in a Randomized Block Design

Published online by Cambridge University Press:  01 January 2025

Thomas P. Hettmansperger*
Affiliation:
The Pennsylvania State University

Abstract

This paper treats the problem of testing an ordered hypothesis based on the ranks of the data. The statistical procedures for the randomized block design with more than one observation per cell are derived. Multiple comparisons and estimation procedures are also included.

Type
Original Paper
Copyright
Copyright © 1975 Psychometric Society

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References

Barlow, R. E., Bartholomew, D. J., Bremner, J. M., and Brunk, H. D.. Statistical Inference Under Order Restrictions, 1972, N. Y.: John Wiley and Sons.Google Scholar
Bauer, D. F.. Constructing confidence sets using rank statistics. Journal of the American Statistical Association, 1972, 67, 689690.CrossRefGoogle Scholar
Bernard, A. and Van Elteren, P.. A generalization of the method of m rankings. Indagationes Mathematicae, 1953, 15, 358369.CrossRefGoogle Scholar
Hettmansperger, T. P. and Klimko, L. A.. A note on the convergence of densities. The Annals of Statistics, 1974, 2, 597598.CrossRefGoogle Scholar
Hodges, J. L. Jr. and Lehmann, E. L.. Estimates of location based on rank tests. Annals of Mathematical Statistics, 1963, 34, 598611.CrossRefGoogle Scholar
Hollander, M.. Rank tests for randomized blocks when the alternatives have an a priori ordering. Annals of Mathematical Statistics, 1967, 38, 867877.CrossRefGoogle Scholar
Hollander, M. and Wolfe, D.. Nonparametric Statistical Methods, 1973, N. Y.: John Wiley and Sons.Google Scholar
Lehmann, E. L.. Non-parametric confidence intervals for a shift parameter. Annals of Mathematical Statistics, 1963, 34, 15071512.CrossRefGoogle Scholar
Page, E. B.. Ordered hypotheses for multiple treatments: A significance test for linear ranks. Journal of the American Statistical Association, 1963, 58, 216230.CrossRefGoogle Scholar
Tyron, P. V. and Hettmansperger, T. P.. A class of non-parametric tests for homogeneity against ordered alternatives. The Annals of Statistics, 1973, 1, 10611070.Google Scholar