Interval estimation of the kappa coefficient with binary classification and an equal marginal probability model

We derive a likelihood score method for interval estimation of the intraclass version of the kappa coefficient of agreement with binary classification using a general theory of Bartlett (1953, Biometrika 40, 306-317). By exact evaluation, we investigate statistical properties of the score method, the chi-square goodness-of-fit procedure (Donner and Eliasziw, 1992, Statistics in Medicine 11, 1511-1519; Hale and Fleiss, 1993, Biometrics 49, 523-534), and a crude confidence interval for small and medium sample sizes. Actual coverage percentages of the score and chi-square methods are satisfactorily close to the nominal confidence coefficient, while that of the crude method is quite unsatisfactory. The expected length of the score method is shorter than that of the chi-square procedure when the response rate is very small or very large.