PROBABLE ERROR OF A CORRELATION COEFFICIENT

Abstract

AT the discussion of Mr R. H. Hooker's recent paper "The correlation of the weather and crops" (Journ.Royal Stat.Soc.1907) Dr Shav made an enquiry as to the significance of correlatioti coefficients derived fronm small numbers of cases.His question was answered by Messrs Yule and Hooker and Professor Edgeworth, all of whom considered that Mr Hooker was probably safe in taking .50 as his limit of significance for a sarnple of 21.They did not, however, answer Dr Shaw's question in anty more general way.Now Mr Hooker is not the only statistician who is forced to work with very smiall samples, and until Dr Shaw's question has been properly answered the results of such investigations lack the criterion which would enable us to make full use of them.The present paper, which is ani account of somie sampling experimiients, has two objects: (1) to throw some light by empirical methods on the problem itself, (2) to endeavour to interest mathematicians who have both time and ability to solve it.Before proceeding further, it may be as well to state the problem which occurs in practice, for it is often confused with other allied questions.A random sample has been obtained from an indefinitely large* population and rt calculate'd between two variable characters of the individuals composing the sample.We require the probability that R for the popuilation from which the sample is drawn shall lie between any given limits. It is clear that in order to solve this proble'm we must know two thing…