Simpson’s paradox: A collection of examples from road safety studies and emergency medicine

Abstract

Simpson’s paradox, first described in 1951, denotes a reversal of a difference or ratio when data for several groups are added up. This paper illustrates the paradox by means of examples taken from road safety studies and emergency medicine. These examples are only intended to show how the paradox can arise. It is not known how common the paradox is or how often it goes undetected. If undetected, it can lead to erroneous conclusions, for example that women have a higher accident rate than men, when in each group formed according to annual driving distance the opposite is the case. The reversal of the difference occurs because there is an interaction between gender, driving distance and accident rate. Women drive shorter than men, and shorter driving distances are associated with higher accident rates than longer driving distances.