Since the introduction of Cohen's kappa as a chance-adjusted measure of agreement between two observers, several "paradoxes" in its interpretation have been pointed out. The difficulties occur because kappa not only measures agreement but is also affected in complex ways by the presence of bias between observers and by the distributions of data across the categories that are used ("prevalence"). In this paper, new indices that provide independent measures of bias and prevalence, as well as of observed agreement, are defined and a simple formula is derived that expresses kappa in terms of these three indices. When comparisons are made between agreement studies it can be misleading to report kappa values alone, and it is recommended that researchers also include quantitative indicators of bias and prevalence.