Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-08T11:20:18.174Z Has data issue: false hasContentIssue false
  • English
  • Français

A Nonparametric Test for the Two-Sample Problem

Published online by Cambridge University Press:  01 January 2025

Myles Hollander
Myles Hollander*
Affiliation:
Stanford University
Get access Rights & Permissions [Opens in a new window]

Abstract

Moses has proposed a nonparametric test of the null hypothesis that two samples, say a treatment and a control group, have been drawn from the same population; his test is designed to be sensitive to the alternative hypothesis that the treatment group is extreme in either or both directions as compared with the controls. This paper presents a test of similar character, except that rather than being based on a range of the control group ranks, it depends upon the variance of those ranks. This has the advantage of making ties less troublesome. Tables of significance values are presented for some small sample sizes. A normal approximation is developed and seen to be useful.

Type
Original Paper
Information
Psychometrika , Volume 28 , Issue 4 , December 1963 , pp. 395 - 403
Copyright
Copyright © 1963 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

This research was partially sponsored by a Public Health Biostatistics Training Grant at Stanford University.

†

I wish to thank Professor Lincoln E. Moses of Stanford University for suggesting the problem, and for his invaluable assistance in the preparation of this paper.

References

Barton, D. E. and David, F. N., Fix, E. The polykays of the natural numbers. Biometrika, 1960, 47, 53–59.CrossRefGoogle Scholar
Hoeffding, W. A class of statistics with asymptotically normal distribution. Ann. math. Statist., 1948, 19, 293–325.CrossRefGoogle Scholar
Moses, L. E. A two-sample test. Psychometrika, 1952, 17, 239–247.CrossRefGoogle Scholar
Tukey, J. W. Some sampling simplified. J. Amer. statist. Ass., 1950, 45, 501–519.CrossRefGoogle Scholar