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The method of maximum likelihood is used to derive an estimate ψ for the correlation coefficient in a 2 × 2 contingency table with an underlying bivariate normal distribution. The estimate ψ 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.
M. A. Hamdan (Wed,) studied this question.