The Forward Specialization Coefficient: Distributional Properties and Subgroup Differences

For both public policy and theoretical reasons, criminologists have been interested in the degree to which criminal offenders specialize in particular crimes. Traditionally, offense specialization has been measured with the forward specialization coefficient (FSC). Recently, the FSC has been criticized for being interpretationally obtuse and having no known sampling distribution. In this paper we examine both the interpretational and the statistical properties of the FSC. We conclude that (1) it has an intuitive interpretation that is no less useful than either a standard correlation coefficient or its competitors, (2) its sampling distribution is approximately normal, and (3) the conventional formula for the estimated standard error of the FSC may underestimate the true standard error in some circumstances. With these results behind us, we propose and illustrate both a parametric statistical test for the difference between two independent FSCs and two nonparametric alternatives.