Probable error of a correlation coefficient
At the discussion of Mr. R. H. Hooker's recent paper "The correlation of the weather and crops" (Journ. Royal Stat. SOC. 1907) Dr Shaw made an enquiry as to the significance of correlation coefficients derived from 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 sample of 21. They did not, however, answer Dr Shaw's question in any more general way, Now Mr. Hooker is not the only statistician who is forced to work with very small 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 an account of some sampling experiments, 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.