Testing Serial Crime Events for Randomness in Day‐of‐Week Patterns with Small Samples

This paper discusses exact tests for evaluating whether a series of offences are randomly distributed across days of the week for small sample sizes. The context is if an analyst has identified a series of related events, can the analyst determine if those events are randomly distributed with respect to the day‐of‐week given only a few offences? This paper develops exact reference distributions because the number of potential permutations is small, and this research finds that the likelihood ratio G‐test under realistic circumstances is quite powerful. Only three crimes need to occur on the same day of the week to reject the null. Several examples of using the test under realistic circumstances are illustrated; a series of thefts of catalytic converters where the exact dates are unknown, gang shootings, and arsons over a year. Copyright © 2015 John Wiley & Sons, Ltd.