What Are the Odds? Modern Relevance and Bayes Factor Solutions for MacAlister’s Problem From the 1881 Educational Times

In 1881, Donald MacAlister posed a problem in the Educational Times that remains relevant today. The problem centers on the statistical evidence for the effectiveness of a treatment based on a comparison between two proportions. A brief historical sketch is followed by a discussion of two default Bayesian solutions, one based on a one-sided test between independent rates, and one on a one-sided test between dependent rates. We demonstrate the current-day relevance of MacAlister’s original question with a modern-day example about the effectiveness of an educational program.