We describe a data-driven discovery method that leverages Simpson's paradox to uncover interesting patterns in behavioral data. Our method systematically disaggregates data to identify subgroups within a population whose behavior deviates significantly from the rest of the population. Given an outcome of interest and a set of covariates, the method follows three steps. First, it disaggregates data into subgroups, by conditioning on a particular covariate, so as minimize the variation of the outcome within the subgroups. Next, it models the outcome as a linear function of another covariate, both in the subgroups and in the aggregate data. Finally, it compares trends to identify disaggregations that produce subgroups with different behaviors from the aggregate. We illustrate the method by applying it to three real-world behavioral datasets, including Q &A site Stack Exchange and online learning platforms Khan Academy and Duolingo.
This paper addresses the discovery of surprising patterns. Recently, several authors have addressed the task of discovering surprising prediction rules. However, we do not focus on prediction rules, but rather on a quite different kind of pattern, namely the occurrence of Simpson’s paradox. Intuitively, the fact that this is a paradox suggests that it has a great potential to be a surprising pattern for the user. With this motivation, we make the detection of Simpson’s paradox the central goal of a data mining algorithm explicitly designed to discover surprising patterns. We present computational results showing surprising occurrences of the paradox in some public-domain data sets. In addition, we propose a method for ranking the discovered instances of the paradox in decreasing order of estimated degree of surprisingness.