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

Abstract

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? One can develop exact reference distributions since the number of potential permutations are small, and I find that the likelihood ratio G-test under realistic circumstances is quite powerful. One need only three crimes to occur on the same day of the week to reject the null. I provide several examples of using the test under realistic circumstances; a series of thefts of catalytic converters where the dates are unknown, gang shootings during a year, and arsons.

Keywords: exact-tests, interval-censored, circular, aoristic, serial-crime