Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-08T16:22:47.404Z Has data issue: false hasContentIssue false
  • English
  • Français

Point Biserial Correlation Coefficient and its Generalization

Published online by Cambridge University Press:  01 January 2025

S. Das Gupta
S. Das Gupta*
Affiliation:
Indian Statistical Institute, Calcutta
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem of measuring the association between two characters, one quantitative and the other qualitative, is discussed. The formula for the large sample standard error of the point biserial correlation coefficient under general conditions is derived. The point multiserial correlation coefficient is introduced and some of its properties are examined. Tests of different hypotheses appropriate to these types of problems are formulated.

Type
Original Paper
Information
Psychometrika , Volume 25 , Issue 4 , December 1960 , pp. 393 - 408
Copyright
Copyright © 1960 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

*

I wish to pay my sincerest thanks to Dr. C. R. Rao, Dr. S. K. Mitra, and the reviewers for their valuable suggestions.

†

Now at the University of North Carolina

References

Cramer, H. Mathematical methods of statistics, Princeton: Princeton Univ. Press, 1946.Google Scholar
Cureton, E. E. Rank-biserial correlation. Psychometrika, 1956, 21, 287–290.CrossRefGoogle Scholar
Das Gupta, S. A note on weighting response categories. Proc. Indian Sci. Congr. Session, 1959. (Abstract).Google Scholar
Fisher, R. A. Statistical methods for research workers (11th ed.), London: Oliver and Boyd, 1950.Google Scholar
Guilford, J. P. Psychometric methods (2nd ed.), New York: McGraw-Hill, 1954.Google Scholar
James, G. S. Tests of linear hypotheses in univariate and multivariate analysis when the ratio of the population variances are known. Biometrika, 1954, 41, 19–43.Google Scholar
Kendall, M. G. The advanced theory of statistics. Vol. II. (3rd ed.), London: Griffin, 1959.Google Scholar
Lev, J. The point biserial coefficient of correlation. Ann. math. Statist., 1949, 20, 125–126.CrossRefGoogle Scholar
Roy, S. N. Some aspects of multivariate analysis, New York: Wiley, 1957.Google Scholar
Siegel, S. Nonparametric statistics for the behavioral sciences, New York: McGraw-Hill, 1956.Google Scholar
Tate, R. F. The biserial and point biserial correlation coefficient. Univ. North Carolina, Inst. of Statist., Mimeo. ser. 14, 1949.Google Scholar
Tate, R. F. Correlations between a discrete and a continuous chance variable. Ann. math. Statist., 1954, 25, 603–607.CrossRefGoogle Scholar
Wherry, R. J. and Taylor, E. K. The relation of multiserial eta to other measures of correlation. Psychometrika, 1946, 11, 155–162.CrossRefGoogle ScholarPubMed