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Statistical Inference Based on Ranks

Published online by Cambridge University Press:  01 January 2025

Thomas P. Hettmansperger  and
Joseph W. McKean
Thomas P. Hettmansperger*
Affiliation:
The Pennsylvania State University
Joseph W. McKean
Affiliation:
The University of Texas, Dallas
*
Requests for reprints should be sent to Thomas P. Hettmansperger, Department of Statistics, Pond Lab., The Pennsylvania State University, University Park, Pennsylvania, 16802.
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Abstract

This paper develops a unified approach, based on ranks, to the statistical analysis of data arising from complex experimental designs. In this way we answer a major objection to the use of rank procedures as a major methodology in data analysis. We show that the rank procedures, including testing, estimation and multiple comparisons, are generated in a natural way from a robust measure of scale. The rank methods closely parallel the familiar methods of least squares, so that estimates and tests have natural interpretations.

Keywords

robust estimatesefficient testsmultiple comparisonslinear modelsensitivity curves

Information

Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 1 , March 1978 , pp. 69 - 79
Copyright
Copyright © 1978 The Psychometric Society

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Footnotes

This research was supported in part by grant MCS76-07292 from the National Science Foundation.

References

Reference Note

Hettmansperger, T. P. & McKean, J. W. K step rank procedures in the linear model. Manuscript submitted for publication, 1977.Google Scholar

References

Anderson, N. H. Scales and statistics: Parametric and non-parametric. Psychological Bulletin, 1961, 58, 305–316.10.1037/h0042576CrossRefGoogle Scholar
Bickel, P. J. On some robust estimates of location. Annals of Mathematical Statistics, 1965, 36, 847–858.10.1214/aoms/1177700058CrossRefGoogle Scholar
Hettmansperger, T. P. & McKean, J. W. Computational problems involved in analysis of linear models based on ranks. Proceedings of the Statistical Computation Section of the American Statistical Association, 1976, 88-94.Google Scholar
Hettmansperger, T. P. & McKean, J. W. A robust alternative based on ranks to least squares in analyzing linear models. Technometrics, 1977, 19, 275–284.CrossRefGoogle Scholar
Hodges, J. L. Jr. & Lehmann, E. L. Estimation of location based on rank tests. Annals of Mathematical Statistics, 1963, 34, 598–611.10.1214/aoms/1177704172CrossRefGoogle Scholar
Huber, P. J. Robust estimation of a location parameter. Annals of Mathematical Statistics, 1964, 35, 73–101.10.1214/aoms/1177703732CrossRefGoogle Scholar
Huber, P. J. Robust statistics: A review. Annals of Mathematical Statistics, 1972, 43, 1041–1067.CrossRefGoogle Scholar
Jaeckel, L. A. Estimating regression coefficients by minimizing the dispersion of the residuals. Annals of Mathematical Statistics, 1972, 43, 1449–1458.CrossRefGoogle Scholar
Lehmann, E. L. Nonparametrics: Statistical methods based on ranks, 1975, San Francisco: Holden-Day.Google Scholar
McKean, J. W. and Hettmansperger, T. P. Tests of hypothesis based on ranks in the general linear model. Communications in Statistics, 1976, A5(8), 693–709.CrossRefGoogle Scholar
McKean, J. W. and Ryan, T. A. Jr. An algorithm for obtaining confidence intervals and point estimates based on ranks in the two-sample location problem. ACM Trans. Math. Software, 1977, 3(2), 183–185.CrossRefGoogle Scholar
Miller, R. G. Jr. Simultaneous statistical inference, 1966, New York: McGraw-Hill.Google Scholar
Wainer, H. & Thissen, D. Three steps towards robust regression. Psychometrika, 1976, 41, 9–34.10.1007/BF02291695CrossRefGoogle Scholar