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On the Large Sample Distributions of Modified Sample Biserial Correlation Coefficients

Published online by Cambridge University Press:  01 January 2025

Edward J. Bedrick
Edward J. Bedrick*
Affiliation:
University of New Mexico
*
Requests for reprints should be sent to Edward J. Bedrick, Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131.
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Abstract

The asymptotic distributions of Brogden's and Lord's modified sample biserial correlation coefficients are derived. The asymptotic variances of these estimators are evaluated for bivariate normal populations and compared to the asymptotic variance of the maximum likelihood estimator.

Keywords

biserial correlationorder statistics
Type
Original Paper
Information
Psychometrika , Volume 55 , Issue 2 , June 1990 , pp. 217 - 228
Copyright
Copyright © 1990 The Psychometric Society

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Footnotes

The author would like to thank the referees for several suggestions which improved the presentation of the paper.

References

Brogden, Hubert E. (1949). A new coefficient: Application to biserial correlation and to estimation of selective effciency. Psychometrika, 14, 169–182.CrossRefGoogle Scholar
Clemans, W. V. (1958). An index of item-criterion relationship. Educational and Psychological Measurement, 18, 167–172.CrossRefGoogle Scholar
Johnson, N. L., & Kotz, S. (1970). Distributions in statistics: Continuous multivariate distributions, New York: John Wiley & Sons.Google Scholar
Koopman, R. F. (1983). On the standard error of the modified biserial correlation. Psychometrika, 48, 639–641.CrossRefGoogle Scholar
Kraemer, H. C. (1981). Modified biserial correlation coefficients. Psychometrika, 46, 275–282.CrossRefGoogle Scholar
Lord, F. M. (1963). Biserial estimates of correlation. Psychometrika, 28, 81–85.CrossRefGoogle Scholar
Pearson, K. (1909). On a new method of determining the correlation between a measured character A and a character B. Biometrika, 7, 96–105.CrossRefGoogle Scholar
Prince, B. M., & Tate, R. F. (1966). Accuracy of maximum likelihood estimates of correlation for a biserial model. Psychometrika, 31, 85–92.CrossRefGoogle Scholar
Serfling, R. J. (1980). Approximation theorems of mathematical statistics, New York: John Wiley & Sons.CrossRefGoogle Scholar
Shorack, G. R. (1974). Random means. Annals of Statistics, 2, 661–675.CrossRefGoogle Scholar
Tate, R. F. (1955). Applications of correlation models for biserial data. Journal of the American Statistical Association, 50, 1078–1095.CrossRefGoogle Scholar