Next to counting, averaging is the most basic and important practice in statistics. For over 150 years it was thought that nothing was uniformly better than the sample average for the purposes of estimation or prediction. In 1955, Charles Stein proved this wasn’t true when considering three or more independent unobservable quantities. In 1961, Willard James and Charles Stein proposed an alternative estimator – the James-Stein estimator – which improved on the simple averaging approach no matter what the true values of the unobservable quantities. Although Stein’s work was initially met with resistance and was slow to be accepted among statisticians, its principal idea is now used widely across statistics and evidence-based medicine.

In this talk, I will explain Stein’s work, the paradox and some of its more controversial results and consider the implications for evidence-based medicine.