Detecting the contagion effect in mass killings; a constructive example of the statistical advantages of unbinned likelihood methods

Background: When attempting to statistically distinguish between a null and an alternative hypothesis, many researchers in the life and social sciences turn to binned statistical analysis methods, or methods that are simply based on the moments of a distribution (such as the mean, and variance). These methods have the advantage of simplicity of implementation, and simplicity of explanation. Methods: In 2015, Towers et al published a paper that quantified the long-suspected contagion effect in mass killings. However, in 2017, Lankford & Tomek subsequently published a paper, based upon the same data, that claimed to contradict the results of the earlier study. The former used unbinned likelihood methods, and the latter used binned methods, and comparison of distribution moments. Conclusions: When an analysis cannot distinguish between a null and alternate hypothesis, care must be taken to ensure that the analysis methodology itself maximizes the use of information in the data that can distinguish between the two hypotheses.