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Some Tests of Significance, Treated by the Theory of Probability

Published online by Cambridge University Press:  24 October 2008

Harold Jeffreys*
St John's College


It often happens that when two sets of data obtained by observation give slightly different estimates of the true value we wish to know whether the difference is significant. The usual procedure is to say that it is significant if it exceeds a certain rather arbitrary multiple of the standard error; but this is not very satisfactory, and it seems worth while to see whether any precise criterion can be obtained by a thorough application of the theory of probability.

Research Article
Copyright © Cambridge Philosophical Society 1935

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* Jeffreys, , Proc. Camb. Phil. Soc. 29 (1933), 83–7.Google Scholar

* dp in this expression for a probability means the proposition that p lies in a particular range of length dp.

This is true throughout the paper in analogous pairs of equations.

* Jeffreys, , Scientific Inference, 1931 Google Scholar, Lemma II, equation (8).

* Jeffreys, , Scientific Inference, 6670.CrossRefGoogle Scholar

The analogy is illustrative and not complete. y = 0 here would correspond in Section I to (p − ½) kε = (p′ − ½) k′ε′, not to p = p′.

* Jeffreys, , Proc. Roy. Soc. A, 137 (1932), 7887.Google Scholar

* Cf. Brunt, , Combination of observations (1931), 165.Google Scholar

* Walker, , Indian Meteor. Mem. 21 (1914)Google Scholar; Q.J.R. Met. Soc. 51 (1925), 337346 Google Scholar, and later papers.