Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-01-07T18:27:45.517Z Has data issue: false hasContentIssue false
  • English
  • Français

Modified Biserial Correlation Coefficients

Published online by Cambridge University Press:  01 January 2025

Helena Chmura Kraemer
Helena Chmura Kraemer*
Affiliation:
Stanford University
*
Reprint requests should be addressed to Helena Chmura Kraemer, Ph.D., Department of Psychiatry and Behavioral Sciences, Stanford University, Stanford, California 94305.
Get access Rights & Permissions [Opens in a new window]

Abstract

Asymptotic distribution theory of Brogden's form of biserial correlation coefficient is derived and large sample estimates of its standard error obtained. Its efficiency relative to the biserial correlation coefficient is examined. Other modifications of the statistic are evaluated, and on the basis of these results, recommendations for choice of estimator of biserial correlation are presented.

Keywords

biserial correlationefficiency
Type
Original Paper
Information
Psychometrika , Volume 46 , Issue 3 , September 1981 , pp. 275 - 282
Copyright
Copyright © 1981 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

Supported by the National Institute of Mental Health Specialized Research Center Grant #MH-30854 and by the National Institute of Mental Health Grant #MH-11028.

References

Brogden, Hubert E. A new coefficient: Application to biserial correlation and to estimation of selective efficiency. Psychometrika, 1949, 14, 169–182.CrossRefGoogle ScholarPubMed
Clemans, W. V. An index of item-criterion relationship. Educational and Psychological Measurement, 1958, 18, 167–172.CrossRefGoogle Scholar
Cramer, H. Mathematical Methods of Statistics, 1946, Princeton: Princeton University Press.Google Scholar
Cureton, E. E. Rank biserial correlation. Psychometrika, 1956, 21, 287–290.CrossRefGoogle Scholar
Cureton, E. E. Rank biserial correlation when ties are present. Educational and Psychological Measurement, 1968, 28, 77–79.CrossRefGoogle Scholar
DasGupta, S. Point biserial correlation coefficient and its generalization. Psychometrika, 1960, 25, 393–408.Google Scholar
Dudek, F. J. A comparison of biserial r with Pearson r. Educational and Psychological Measurement, 1952, 12, 759–766.CrossRefGoogle Scholar
Glass, Gene V. Note on rank biserial correlation. Educational and Psychological Measurement, 1966, 26, 623–631.CrossRefGoogle Scholar
Kraemer, Helena Chmura Robustness of the distribution theory of the product moment correlation coefficient. Journal of Educational Statistics, 1980, 5, 115–128.Google Scholar
Lev, J. The point biserial coefficient of correlation. Annals of Mathematical Statistics, 1949, 20, 125–126.CrossRefGoogle Scholar
Lord, Frederic M. Biserial estimates of correlation. Psychometrika, 1963, 28, 81–85.CrossRefGoogle Scholar
Olkin, I., Tate, R. F. Multivariate correlation models with mixed discrete and continuous variables. Annals of Mathematical Statistics, 1961, 32, 448–465.CrossRefGoogle Scholar
Pearson, Karl On a new method for determining the correlation between a measured character A and a character B, of which only the percentage of cases wherein B exceeds (or falls short of) a given intensity is recorded for each grade of A. Biometrika, 1908, 7, 96–105.CrossRefGoogle Scholar
Pearson, Karl On a method of determining correlation, when one variable is given by alternative and the other by multiple categories. Biometrika, 1910, 7, 248–257.CrossRefGoogle Scholar
Soper, H. E. On the probable error of the bi-serial expression for the correlation coefficient. Biometrika, 1914, 10, 384–384.CrossRefGoogle Scholar
Stanley, Julian C. An important similarity between biserial r and the Brogden-Cureton-Glass biserial r for ranks. Educational and Psychological Measurement, 1968, 28, 249–253.CrossRefGoogle Scholar
Tate, Robert F. Correlation between a discrete and a continuous variable: Point biserial correlation. Annals of Mathematical Statistics, 1954, 25, 603–607.CrossRefGoogle Scholar
Tate, Robert F. Applications of correlation models for biserial data. Journal of the American Statistical Association, 1955, 50, 1078–1095.CrossRefGoogle Scholar
Tate, Robert F. The theory of correlation between two continuous variables when one is dichotomized. Biometrika, 1955, 42, 205–216.CrossRefGoogle Scholar
Wilson, Victor L. Critical values of the rank biserial correlation coefficient. Educational and Psychological Measurement, 1976, 36, 297–300.CrossRefGoogle Scholar