Published results on the use of the kappa coefficient of agreement have traditionally been concerned with situations where a large number of subjects is classified by a small group of raters. The coefficient is then used to assess the degree of agreement among the raters through hypothesis testing or confidence intervals. A modified kappa coefficient of agreement for multiple categories is proposed and a parameter-free distribution for testing null agreement is provided, for use when the number of raters is large relative to the number of categories and subjects. The large-sample distribution of kappa is shown to be normal in the nonnull case, and confidence intervals for kappa are provided. The results are extended to allow for an unequal number of raters per subject.