In this paper we discuss a method for assessing agreement among raters who are scoring the number of times, a specified event occurs. In such cases, it seems reasonable to define agreement in terms of raters' behaviours in correctly identifying responses which have in fact occurred, and in their falsely counting responses which have not. We exploit the discrete nature of the response variable, and examine a class of models for mean response assuming an underlying Poisson distribution. Test statistics are given for deciding on the applicability of the models, and whether there is agreement with respect to correctly detecting responses, as well as with falsely scoring responses.