Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-01-08T10:25:43.397Z Has data issue: false hasContentIssue false
  • English
  • Français

An Estimation of True Scores in the Case of Items Scored on a Continuous Scale

Published online by Cambridge University Press:  01 January 2025

A. B. L. Srivastava  and
Harold Webster
A. B. L. Srivastava
Affiliation:
Department of Psychological Foundations, National Institute of Education, Delhi, India
Harold Webster
Affiliation:
Columbia University Teachers College Team, Delhi, India
Get access Rights & Permissions [Opens in a new window]

Abstract

For the tests in which the score on an item is not restricted to 0 and 1, but is any number on a continuous scale, a procedure for estimating an examinee's true score is given. For the case of 0, 1 item scoring this problem was considered by Lord [1959]. Following Lord, the least squares estimation procedure is used and the regression coefficient is obtained, which is compared with the generalized KR(20) and KR(21) formulas. Also, results are discussed using analysis of variance models.

Type
Original Paper
Information
Psychometrika , Volume 32 , Issue 3 , September 1967 , pp. 327 - 338
Copyright
Copyright © 1967 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

*

Now at Brooklyn College of the City University of New York.

References

Cronbach, L. J. Coefficient alpha and the internal structure of tests. Psychometrika, 1951, 16, 297–334.CrossRefGoogle Scholar
Gleser, G. C., Cronbach, L. J., and Rajaratnam, N. Generalizability of scores influenced by multiple sources of variance. Psychometrika, 1965, 30, 395–418.CrossRefGoogle ScholarPubMed
Kuder, G. F. and Richardson, M. W. The theory of the estimation of test reliability. Psychometrika, 1937, 2, 151–160.CrossRefGoogle Scholar
Lord, F. M. Sampling fluctuations resulting from the sampling of items. Psychometrika, 1955, 20, 1–22.CrossRefGoogle Scholar
Lord, F. M. Statistical inference about true scores. Psychometrika, 1959, 24, 1–17.CrossRefGoogle Scholar
Rajaratnam, N. Reliability formulas for independent decision data when reliability data are matched. Psychometrika, 1960, 25, 261–271.CrossRefGoogle Scholar
Webster, H. A generalization of Kuder-Richardson reliability formula 21. Educational and psychological Measurement, 1960, 20, 131–138.CrossRefGoogle Scholar
Webster, H. and Bereiter, C. The reliability of changes measured by mental test scores. In Harris, C. W. (Eds.), Problems in measuring Change, Madison: University of Wisconsin Press, 1963.Google Scholar