Understanding Simpson's Paradox

Abstract

Simpson's paradox is often presented as a compelling demonstration of why we need statistics education in our schools. It is a reminder of how easy it is to fall into a web of paradoxical conclusions when relying solely on intuition, unaided by rigorous statistical methods. In recent years, ironically, the paradox assumed an added dimension when educators began using it to demonstrate the limits of statistical methods, and why causal, rather than statistical considerations are necessary to avoid those paradoxical conclusions (Arah, 2008; Pearl, 2009, pp. 173-182; Wasserman, 2004).

My comments are divided into two parts. First, I will give a brief summary of the history of Simpson's paradox and how it has been treated in the statistical literature in the past century. Next I will ask what is required to declare the paradox "resolved," and argue that modern understanding of causal inference has met those requirements.