When there are confounders in reliability studies, failing to stratify data to account for these confounding e!ects may produce a misleading estimate of the interrater agreement. In this paper, we focus discussion on interval estimation of kappa for measuring agreement between two raters with strati"ed data. Using Monte Carlo simulation, we compare four asymptotic interval estimators of kappa for strati"ed data: estimator (1), a weighted average of the stratum-speci"c kappa estimates with weights equal to the inverse of the estimated asymptotic variances of these estimates; the two estimators, ( 2) and ( 3), with use of the logarithmic and the square root transformations, respectively, and a principle similar as used in estimator (1); estimator (4), a weighted average of the stratum-speci"c kappa estimates with weights equal to stratum sizes. We "nd that while the coverage probability of the "rst three interval estimators (1)}(3) can often be less than the desired con"dence level, the fourth interval estimator (4) consistently performs well in all the situations considered here. We further "nd that when the underlying is moderate (0)30) )0)50), we can substantially improve the performance of the "rst three estimators by using a point estimator recently proposed elsewhere for in estimation of weights. Because interval estimator (4) outperforms the other three estimators in a variety of situations, we recommend this estimator for general use.