Testing Consistency of Two Histograms

Several approaches to testing the hypothesis that two histograms are drawn from the same distribution are investigated. We note that single-sample continuous distribution tests may be adapted to this two-sample grouped data situation. The difficulty of not having a fully-specified null hypothesis is an important consideration in the general case, and care is required in estimating probabilities with “toy” Monte Carlo simulations. The performance of several common tests is compared; no single test performs best in all situations.