No. 589] 



NOTES AND LITERATURE 



61 



For several years critical workers have realized that very little 

 reliance is to be placed upon Yule's very simple coefficient of 

 association. This coefficient and another measure of correlation 

 "the theoretical value of r" proposed in his " Introduction to 

 the Theory of Statistics" have been discussed by Heron. 34 

 Pearson and Heron 35 and Pearson 36 have gone into these methods 

 and others proposed by Yule 37 in a masterly way. To discuss 

 this memoir alone would require far more than the space avail- 

 able for this general index of the correlation methods. Their 

 treatment can leave no doubt— if any existed in the minds of 

 those who have tried to use these formulae in serious statistical 

 work — that except in very special cases all these association and 

 colligation formulae are likely to work harm rather than to be of 

 service in the hands of the biologist. 



This demonstration of the untrustworthiness of the various 

 substitutes for the correlation coefficient practically throws us 

 back upon the old four-fold method of Pearson, and upon another 

 novel method to be discussed in a moment. The difficulty of com- 

 putation has been one of the greatest obstacles in the way of the 

 more general application of this method and has frequently 

 resulted in the substitution of the less reliable coefficient of as- 

 sociation. The necessary labor of calculation has been much 

 reduced by two series of tables by Everitt. 38 



The determination of the probable error of the coefficient of 

 correlation calculated from the four-fold grouping has always 

 been excessively laborious. While four-fold correlations have 

 been calculated in hundreds of cases, the determination of the 

 probable error has been made for less than a hundred of the 

 coefficients. Pearson 39 has now given tables to facilitate the cal- 



3* Heron, D., "The Danger of Certain Formula? Suggested as Substitutes 

 tor the Correlation Coefficient/' Biometrika, 8: 109-122, 1911. 



35 Pearson, K., and D. Heron, "On Theories of Association," Biometrilca, 

 9: 159-315, 1913. ' 



38 Pearson, K., "Note on the Surface of Constant Association » Bio- 

 metrika, 9: 534-537, 1913. 



■vllZ U}e '„ G T V '' "° n thG Meth0ds of Meas ^g Association between Two 

 vanates, Jour. Boy. Stat. Soc, 75: 579-641, 1912. 



relate T'J' T," " Tabl6S ° f tbe Tetra <*°™ Functions for Four-fold Cor- 

 fo vL ft' „ Bi0metri * a > ^-451, 1909; "Supplementary Tables 

 ZriZ 7 ^ C 9 0rrelation Coefficient from Tetrachoric Groupings," Bio- 

 SrfdLf" ' 1912 ' A1S ° in " Tables for statisticians a^ Bio- 



39 Pearson, K, "On the Probable Error of a Coefficient of Correlation as 



