ON A NOVEL METHOD OF REGARDING ASSOCIATION 15 



are determined to two figures. This abac was constructed in the following manner : 

 Accurate curves were drawn of the values of each „o-^ of log x". From these curves 

 the values of log^^ were read off for each value of r proceeding by -01, from "05 to 

 *95. It was then possible to plot the family of curves which for each r give the 

 relationship of logx' and „o-^. I owe this excellent diagram to Mr G. H. Soper. 

 The bulk of the laborious calculating work on the tables has been carried out 

 by Miss Julia Bell. 



In the course of our investigations two additional tables have been calculated. 

 In the first place it was needful to extend Sheppard's Tables far beyond the limits of 

 published work on the probability integral in order to compare how far it was possible 

 to trust the Gaussian to give the distribution of frequency of correlation coefficients 

 obtained by sampling independent material. As we have seen, the Gaussian is 

 of no service for this purpose except for very low values of r [e.g. 0*1 or less). But 

 the table has independently considerable value, and most statisticians will remember 

 cases when they have had laboriously to calculate 



J2njx 



•*^'d« 



beyond the usual limit of a; = 5. I reproduce this table here as Table VI. 

 calculated by aid of Scholmilch's formula*, i.e. 



^/27^ l^;' x' (af + 2) x' (a;^ + 2) {x' + 4) 



5 9 



It was 



j2TrJx 



e-*^Va; = 



' x^x'' + 2) {x^ + 4:) {x' + 6)'^ x' {x^ + 2) {x' + A) {x' + 6) {x' +8) 



129 



'+10) -J 



x' {af + 2) {x? + A) {x' + 6) {af + 8) (x' 

 and the table gives — log F, for ease of interpolation. It was calculated to seven 

 decimal places, but only five are retained, as the seventh figure was not trustworthy 

 and occasionally the sixth is doubtful. 



It remains to examine some of the correlations found for fourfold tables by this 

 novel process, and to compare the value as found by the assumption of Gaussian 

 frequency. 



Illustration I. The following table is given by me for good and bad temper in 

 pairs of brothers {Phil. Trans. Vol. 195 A, p. 147). 



First Brother 



o 

 u 



OQ 



* Compendium der hoheren Analysis, Bd. ii. S. 270, Braunschweig, 1879. 



