Basic to many psychological investigations is the question of agreement between observers who independently categorize people. Several recent studies have proposed measures of agreement when a set of nominal scale categories have been pre-defined and imposed on both observers. This study, in contrast, developes a measure of agreement for settings where observers independently define their own categories. Thus, it is possible for observers to delineate different numbers of categories, with different names. Computational formulae for the mean and variance of the proposed agreement measure are given; further, a statistic with a large-sample normal distribution is suggested for testing the null hypothesis of random agreement. A computer based comparison of the large sample approximation with the exact distribution of the test statistic shows a generally good fit, even for moderate sample sizes. Finally, a worked example involving two psychologists' classifications of children illustrates the computations. (Author)