The First Formal Test of Significance

Comments on Arbuthnott (1710)
  • H. A. David
  • A. W. F. Edwards
Part of the Springer Series in Statistics book series (SSS)


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.


Royal Society Genetical Theory Prob Ability Natural Theology Male Birth 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aitken, G.A. (1892). The Life and Works of John Arbuthnot. Clarendon Press, Oxford.Google Scholar
  2. Anscombe, F.J. (1981). Computing in Statistical Science through APL. Springer, New York.zbMATHCrossRefGoogle Scholar
  3. Arbuthnott, J. (1710). An argument for Divine Providence, taken from the constant regularity observ’d in the births of both sexes. Phil. Trans., 27, 186–190.CrossRefGoogle Scholar
  4. Bellhouse, D.R. (1989). A manuscript on chance written by John Arbuthnot. Intern. Statist. Rev. 57, 249–259.zbMATHCrossRefGoogle Scholar
  5. Bentley, R. (1693). The Folly and Unreasonableness of Atheism. Reprinted in Dyce (1838).Google Scholar
  6. Dyce, A. (ed.) (1838). The Works of Richard Bentley D.D., Vol. 3. Macpherson, London.Google Scholar
  7. Edwards, A.W.F. (1987). Pascal’s Arithmetical Triangle. Griffin, London and Oxford University Press, New York.zbMATHGoogle Scholar
  8. Edwards, A.W.F. (1998). Natural selection and the sex ratio: Fisher’s sources. American Naturalist, 151, 564–569.CrossRefGoogle Scholar
  9. Fisher, R.A. (1930). The Genetical Theory of Natural Selection. Clarendon Press, Oxford; 2nd edn. Dover, New York, 1958; variorum edn. Oxford University Press, 1999.zbMATHGoogle Scholar
  10. Fisher, R.A. (1935). The Design of Experiments. Oliver & Boyd, Edinburgh.Google Scholar
  11. Hacking, I. (1965). Logic of Statistical Inference. Cambridge University Press.zbMATHGoogle Scholar
  12. Hacking, I. (1975). The Emergence of Probability. Cambridge University Press.zbMATHGoogle Scholar
  13. Hald, A. (1990). A History of Probability and Statistics and Their Applications before 1750. Wiley, New York.zbMATHCrossRefGoogle Scholar
  14. Moivre, A. de (1718). The Doctrine of Chances. Pearson, London.Google Scholar
  15. Paley, W. (1802). Natural Theologyor Evidences of the Existence and Attributes of the Deity Collected from the Appearances of Nature. Vincent, Oxford.Google Scholar
  16. Shoesmith, E. (1985). Nicholas Bernoulli and the argument for Divine Providence. Intern. Statist. Rev., 53, 255–259.zbMATHCrossRefGoogle Scholar
  17. Shoesmith, E. (1987). The continental controversy over Arbuthnot’s argument for Divine Providence. Eistoria Mathematica, 14, 133–146.MathSciNetzbMATHCrossRefGoogle Scholar
  18. Todhunter, I. (1865). A History of the Mathematical Theory of Probability. Macmillan, Cambridge. [Reprinted by Chelsea, New York, 1949, 1965.]Google Scholar
  19. Westfall, R.S. (1980). Never at Rest—A Biography of Newton. Cambridge University Press.Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • H. A. David
    • 1
  • A. W. F. Edwards
    • 2
  1. 1.Statistical Laboratory and Department of StatisticsIowa State UniversityAmesUSA
  2. 2.Gonville and Caius CollegeCambridgeUK

Personalised recommendations