The First Probability-Based Hypothesis Test and God

John Arbuthnot (1667 – 1735) was born in Aberdeen, Scotland but lived in London for a significant part of his life. He was a physician, writer, political satirist and somewhat less of a mathematician and probabilist. He was Queen Anne’s and Prince George’s personal physician and counted literary figures such as Alexander Pope and Jonathon Swift among his close friends. In 1692, Arbuthnot’s Of the Laws of Chance, a translation into English of Christiaan Huygens’ work on probability, was published (Diaconis and Skyrms 2018). The volume sold well (going through four editions), contained some original work, and provided practical gambling applications (Heyde and Seneta 2001). Arbuthnot was politically active and supported and wrote in favor of the Act of Union between England and Scotland that took effect in 1707.3 He created the allegorical character John Bull as a depiction of England in his satirical pamphlet Law is a Bottomless Pit (1712a).4 Arbuthnot was elected a Fellow of the Royal Society in 1704 to which he read a paper on hypothesis testing in 1710. That paper, published in the Society’s Philosophical Transactions (1712b), is the subject of this historical note.