Stein's paradox

Dr Jason Oke, Principal Statistician at Abbott Diabetes Care, was previously a senior statistician at the Nuffield Department of Primary Care Health Sciences, University of Oxford. He has a wealth of experience in applying statistics and data analysis across many health care domains. He is passionate about advancing evidence-based health care practice and policy through rigorous research and teaching.

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.