I’ve uploaded a new paper, Testing for Randomness in Day of Week Crime Sprees with Small Samples, to SSRN. The abstract is below:
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 given context is if a crime analyst has identified a series of events that are committed by the same offender(s), can the analyst determine if those events are randomly distributed with respect to the day of week given only a few offences? I detail how one can develop exact reference distributions since the number of potential permutations are small. I also discuss the power of the chi^2 and Kuiper’s V test for small sample sizes, and give an example of hypothesis testing when crimes have uncertain days of occurrence.
Here is an example graph of the power of the tests under different alternate hypotheses of crimes only having probability of being committed on a certain subset of days in the week. Comments on the paper would be wonderful (I will have to bug someone to give me some pre peer-review feedback) – so feel free.