Hostname: page-component-5f745c7db-xx4dx Total loading time: 0 Render date: 2025-01-06T06:13:50.014Z Has data issue: true hasContentIssue false
  • English
  • Français

The Approximate Sampling Distribution of Kuder-Richardson Reliability Coefficient Twenty

Published online by Cambridge University Press:  01 January 2025

Leonard S. Feldt
Leonard S. Feldt*
Affiliation:
State University of Iowa
Get access Rights & Permissions [Opens in a new window]

Abstract

An approximation to the sampling distribution of Kuder-Richardson reliability formula 20 is derived, using its algebraic equivalent obtained through an items-by-subjects analysis of variance. The theoretical distribution is compared to empirical estimates of the sampling distribution to assess how crucial certain assumptions are. The use of the theoretical distribution for testing hypotheses and deriving confidence intervals is illustrated. A table of equations for approximating 80, 90, and 95 per cent confidence intervals is presented with N ranging from 40 to 500.

Type
Original Paper
Information
Psychometrika , Volume 30 , Issue 3 , September 1965 , pp. 357 - 370
Copyright
Copyright © 1965 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

Baker, F. B. Empirical determination of sampling distributions of item discrimination indices and a reliability coefficient, Madison, Wisc.: Univ. Wisconsin, 1962.Google Scholar
Blackburn, H. L. and Benton, A. L. Revised administration and scoring of the digit span test. J. consult. Psychol., 1957, 21, 139–143.CrossRefGoogle ScholarPubMed
Craig, A. T. On the independence of certain estimates of variance. Ann. math. Statist., 1938, 9, 48–55.CrossRefGoogle Scholar
Cronbach, L. J. Coefficient alpha and the internal structure of tests. Psychometrika, 1951, 16, 297–334.CrossRefGoogle Scholar
Dixon, W. J. and Massey, F. J. Introduction to statistical analysis (2nd ed.), New York: McGraw-Hill, 1957.CrossRefGoogle Scholar
Ebel, R. L. Estimation of the reliability of ratings. Psychometrika, 1951, 16, 407–424.CrossRefGoogle Scholar
Gulliksen, H. Theory of mental tests, New York: Wiley, 1950.CrossRefGoogle Scholar
Haggard, E. A. Intraclass correlation and the analysis of variance, New York: Dryden Press, 1958.Google Scholar
Hoyt, C. Test reliability obtained by analysis of variance. Psychometrika, 1941, 6, 153–160.CrossRefGoogle Scholar
Huntsberger, D. V. Elements of statistical inference, Boston: Allyn and Bacon, 1961.CrossRefGoogle Scholar
Jackson, R. W. B. and Ferguson, G. A. Studies on the reliability of tests. Bulletin No. 12, Toronto: Univ. Toronto Press, 1941.Google Scholar
Kuder, G. F. and Richardson, M. W. The theory of the estimation of test reliability. Psychometrika, 1937, 2, 151–160.CrossRefGoogle Scholar
Lindquist, E. F. Design and analysis of experiments in psychology and education, Boston: Houghton Mifflin, 1953.Google Scholar
Lindquist, E. F. Educational measurement, Washington, D.C.: American Council on Education, 1951.Google Scholar
Lord, F. M. Sampling fluctuations resulting from the sampling of test items. Psychometrika, 1955, 20, 1–22.CrossRefGoogle Scholar
Lord, F. M. An empirical study of the normality and independence of errors of measurement in test scores. Psychometrika, 1960, 25, 91–104.CrossRefGoogle Scholar
Mollenkopf, W. G. Variation of the standard error of measurement. Psychometrika, 1949, 14, 189–229.CrossRefGoogle ScholarPubMed
Smith, J. G. and Duncan, A. J. Sampling statistics and applications, New York: McGraw-Hill, 1945.Google Scholar