What Are the Odds? Modern Relevance and Bayes Factor Solutions for MacAlister's Problem From the 1881 Educational Times. (October 2017)

• Record Type: Journal Article
• Authors: Jamil, Tahira; Marsman, Maarten; Ly, Alexander; Morey, Richard D.; Wagenmakers, Eric-Jan
• Is Part Of: Educational and psychological measurement. Volume 77:Number 5(2017:Oct.)
• Page Start: 819
• Page End: 830
• Publication Date: 2017-10
• Subjects: contingency tables -- Bayes factor -- evidence; Educational tests and measurements -- Periodicals; Psychological tests -- Periodicals; 151.205
• DOI: 10.1177/0013164416667980
• Languages: English
• ISSNs: 0013-1644

Abstract

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.