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A Comparison of Generalized and Modified Sample Biserial Correlation Estimators

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, New Mexico, 87131.
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Abstract

In a recent paper, Bedrick derived the asymptotic distribution of Lord's modified sample biserial correlation estimator and studied its efficiency for bivariate normal populations. We present a more detailed examination of the properties of Lord's estimator and several competitors, including Brogden's estimator. We show that Lord's estimator is more efficient for three nonnormal distributions than a generalization of Pearson's sample biserial estimator. In addition, Lord's estimator is reasonably efficient relative to the maximum likelihood estimator for these distributions. These conclusions are consistent with Bedrick's results for the bivariate normal distribution. We also study the small sample bias and variance of Lord's estimator, and the coverage properties of several confidence interval estimates.

Keywords

asymptotic efficiencybiserial correlationconfidence intervalmixed continuous and discrete data
Type
Original Paper
Information
Psychometrika , Volume 57 , Issue 2 , June 1992 , pp. 183 - 201
Copyright
Copyright © 1992 The Psychometric Society

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Footnotes

The author would like to thank the referees for several suggestions that improved the paper.

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