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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bedrick, E. J. (1990). On the large sample distributions of modified sample biserial correlation coefficients.Psychometrika, 55, 217–228.
Brogden, H. E. (1949). A new coefficient: Application to biserial correlation and to estimation of selective efficiency.Psychometrika, 14, 169–182.
Johnson, N. L., & Kotz, S. (1970).Distributions in statistics: Continuous multivariate distributions. New York: John Wiley and Sons.
Kraemer, H. C. (1981). Modified biserial correlation coefficients.Psychometrika, 46, 275–282.
Lord, F. M. (1963). Biserial estimates of correlation.Psychometrika, 28, 81–85.
Miller, R. G., Jr. (1974). The jackknife: A review.Biometrika, 61, 1–16.
Maronna, R. A. (1976). RobustM-estimators of multivariate location and scatter.Annals of Statistics, 4, 51–67.
Pearson, K. (1909). On a new method of determining the correlation between a measured characterA and a characterB.Biometrika, 7, 96–105.
Rao, C. R. (1973).Linear statistical inference and its applications (2nd ed.). New York: John Wiley and Sons.
Snedecor, G. W., & Cochran, W. G. (1978).Statistical methods (6th ed.). Ames, Iowa: The Iowa State University Press.
Soper, H. E. (1913). On the probable error for the biserial expression for the correlation coefficient.Biometrika, 10, 384.
Tate, R. F. (1955). The theory of correlation between two continuous variables when one is dichotomized.Biometrika, 42, 205–216.
Author information
Authors and Affiliations
Additional information
The author would like to thank the referees for several suggestions that improved the paper.
Rights and permissions
About this article
Cite this article
Bedrick, E.J. A comparison of generalized and modified sample biserial correlation estimators. Psychometrika 57, 183–201 (1992). https://doi.org/10.1007/BF02294504
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02294504