The First Formal Test of Significance

Abstract

In the years around 1700 the “argument from design” for the existence of God emerged from the mists of the classical past to become, in the hands of John Arbuthnott, a probability calculation involving the rejection of a null hypothesis on the grounds of the small probability of the observed data given that hypothesis. (The clarifying terminology “null hypothesis” was not coined until 1935, by R.A. Fisher.) The evolution of the argument took place among a small group of Fellows of the Royal Society of London, including Richard Bentley, Abraham de Moivre, Isaac Newton, Samuel Clarke, and William Derham, as well as Arbuthnott himself, leading Hacking (1975, quoting Anders Jeffner) to dub it “Royal Society theology.” By 1718 de Moivre was stating its basis clearly in the Preface to the first edition of The Doctrine of Chances:

Further, The same Arguments which explode the notion of Luck may, on the other side, be useful in some Cases to establish a due comparison between Chance and Design: We may imagine Chance and Design to be as it were in Competition with each other, for the production of some sorts of Events, and may calculate what Probability there is, that those Events should be rather owing to one than to the other.