Simpson's paradox, moderation and the emergence of quadratic relationships in path models: an information systems illustration

Abstract

While Simpson's paradox is well-known to statisticians, it seems to have been largely neglected in many applied fields of research, including the field of information systems. This is problematic because of the strange nature of the phenomenon, the wrong conclusions and decisions to which it may lead, and its likely frequency. We discuss Simpson's paradox and interpret it from the perspective of path models with or without latent variables. We define it mathematically and argue that it arises from incorrect model specification. We also show how models can be correctly specified so that they are free from Simpson's paradox. In the process of doing so, we show that Simpson's paradox may be a marker of two types of co-existing relationships that have been attracting increasing interest from information systems researchers, namely moderation and quadratic relationships.