Simpson's Paradox and Cornfield’s Conditions

Simpson's Paradox occurs when an observed association is spurious – reversed after taking into account a confounding factor. At best, Simpson's Paradox is used to argue that association is not causation. At worst, Simpson's Paradox is used to argue that induction is impossible in observational studies (that all arguments from association to causation are equally suspect) since any association could possibly be reversed by some yet unknown confounding factor. This paper reviews Cornfield's conditions – the necessary conditions for Simpson's Paradox – and argues that a simple-difference form of these conditions can be used to establish a minimum effect size for any potential confounder. Cornfield's minimum effect size is asserted to be a key element in statistical literacy. In order to teach this important concept, a graphical technique was developed to illustrate percentage-point difference comparisons. Some preliminary results of teaching these ideas in an introductory statistics course are presented.