Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-01-08T12:21:54.447Z Has data issue: false hasContentIssue false
  • English
  • Français

Regression Tests for Several Samples

Published online by Cambridge University Press:  01 January 2025

Harold Gulliksen  and
S. S. Wilks
Harold Gulliksen
Affiliation:
The Educational Testing Service and Princeton University
S. S. Wilks
Affiliation:
The Educational Testing Service and Princeton University
Get access Rights & Permissions [Opens in a new window]

Abstract

In many situations it is desirable or necessary to administer a set of tests to several different groups, and to ask if the results obtained in the different groups may be regarded as being essentially the same in some sense. In the case of two variables (one dependent and one independent) one may, for instance, ask if the errors of estimate and the regression lines may be regarded as being the same for the populations from which the different groups are drawn. For this case, the present article considers tests for three hypotheses regarding the populations from which the different groups are drawn: (a) HA, the hypothesis that all standard errors of estimate are equal; (b) HB, the hypothesis that all regression lines are parallel, (assuming HA); and (c) HC, the hypothesis that the regression lines are identical, (assuming HB). Test criteria for these three hypotheses and their sampling theory for large samples are presented. The results are extended to the case of several independent variables. An illustrative problem is presented for two groups, two independent and one dependent variable.

Type
Original Paper
Information
Psychometrika , Volume 15 , Issue 2 , June 1950 , pp. 91 - 114
Copyright
Copyright © 1950 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.)

References

Pearson, E. S., and Wilks, S. S. Methods of statistical analysis appropriate for k samples of two variates. Biometrika, 1933, 25, 353–378.CrossRefGoogle Scholar
Snedecor, , George, W. Statistical methods 3rd Ed.,, Ames, Iowa: The Iowa State College Press, 1940.Google Scholar
Wilks, S. S. Mathematical statistics, Princeton: Princeton University Press, 1943.Google Scholar