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

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.