Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-01-08T09:51:06.417Z Has data issue: false hasContentIssue false
  • English
  • Français

A Comparison of Three Methods of Fitting the Normal Ogive

Published online by Cambridge University Press:  01 January 2025

Elliot M. Cramer
Elliot M. Cramer*
Affiliation:
The Johns Hopkins University
Get access Rights & Permissions [Opens in a new window]

Abstract

The Mueller-Urban method of fitting the normal ogive is derived, and the inadequacies of its inherent assumptions are discussed. This and the unweighted least squares method are compared to the maximum likelihood solution which is shown to be very close to the “ideal” least squares solution. As an empirical demonstration of the superiority of the maximum likelihood solution, random ogives are fitted by all three methods and they are compared on the basis of the expected values and the standard errors of the estimates. It is concluded that the maximum likelihood solution is uniformly superior to the others in all respects.

Type
Original Paper
Information
Psychometrika , Volume 27 , Issue 2 , June 1962 , pp. 183 - 192
Copyright
Copyright © 1962 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 done under Contract Nonr-248(55) between the Office of Naval Research and The Johns Hopkins University. This is Report No. 18 under that contract. Reproduction in whole or in part is permitted for any purpose of the United States Government. This paper is part of a dissertation submitted to The Johns Hopkins University. Part of this work was done while the author was a National Institutes of Health Research Fellow.

†

The author is indebted to Dr. Wendell R. Garner for his valuable advice and encouragement, and to Jerome Cornfield for several helpful discussions.

References

Berkson, J. Tables for use in estimating the normal distribution function by normit analysis. Biometrika, 1957, 44, 411–435.Google Scholar
Cramer, E. M. Fitting the normal ogive on the IBM 650. J. ed. Measmt, 1962, 22, 177–181.Google Scholar
Cramer, E. M. The long-term effects of experience on judgments of loudness. Percept. mot. Skills, 1962, 14, 271–280.CrossRefGoogle Scholar
Cornfield, J. and Mantel, N. Some new aspects of the application of maximum likelihood to the calculation of the dosage response curve. J. Amer. statist. Ass., 1950, 45, 181–210.CrossRefGoogle Scholar
Finney, D. J. The application of probit analysis to the results of mental tests. Psychometrika, 1944, 9, 31–39.CrossRefGoogle Scholar
Finney, D. J. Probit analysis, Cambridge, Eng.: Univ. Press, 1952.Google Scholar
Guilford, J. P. Psychometric methods (2nd ed.), New York: McGraw-Hill, 1954.Google Scholar