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Biometrika 1970 57(1):212-215; doi:10.1093/biomet/57.1.212
© 1970 by Biometrika Trust
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MISCELLANEA

The equivalence of tetrachoric and maximum likelihood estimates of p in 2 × 2 tables

M. A. HAMDAN

Virginia Polytechnic Institute and American University of Beirut

The method of maximum likelihood is used to derive an estimate {psi} for the correlation coefficient in a 2 × 2 contingency table with an underlying bivariate normal distribution. The estimate {psi} is proved to be identical to Pearson's (1900) tetrachoric estimate rt. Hence, we give an approximate expression for the standard error of rt which is much simpler than Pearson's (1913) expression.


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