Simulation-Based Inference: Beyond a Two-Sample Test

Abstract

Using simulation-based methods for introducing statistical inference has received much attention in recent years. Often these are illustrated with experiments comparing two samples where randomization samples are generated by re-assigning the treatment groups at random to see how often the original sample difference is exceeded. This idea can be easily extended to more complicated situations involving relationships among more than just two groups. We discuss how tests for association in a two-way table, differences in means among more than two groups, or the effectiveness of statistical models can also be introduced with the same intuitive framework. Depending on curriculum, these might be done in an introductory course or as part of a second course. We illustrate these methods with several examples, encouraging participants to “click along” with freely available online apps, and show how the simulations help build connections to traditional procedures based on chi-square and F-distributions.

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Teaching with Simulation-Based Inference