S. Senn
Stephen Senn
Head of Competence Center for Methodology and Statistics (CCMS)
Luxembourg Institute of Health
Double Jeopardy?: Judge Jeffreys Upholds the Law*[4]
“But this could be dealt with in a rough empirical way by taking twice the standard error as a criterion for possible genuineness and three times the standard error for definite acceptance”. Harold Jeffreys(1) (p386)
This is the second of two posts on P-values. In the first, The Pathetic P-Value, I considered the relation of P-values to Laplace’s Bayesian formulation of induction, pointing out that that P-values, whilst they had a very different interpretation, were numerically very similar to a type of Bayesian posterior probability. In this one, I consider their relation or lack of it, to Harold Jeffreys’s radically different approach to significance testing. (An excellent account of the development of Jeffreys’s thought is given by Howie(2), which I recommend highly.)
The story starts with Cambridge philosopher CD Broad (1887-1971), who in 1918 pointed to a difficulty with Laplace’s Law of Succession. Broad considers the problem of drawing counters from an urn containing n counters and supposes that all m drawn had been observed to be white. He now considers two very different questions, which have two very different probabilities and writes: Continue reading
