1909-10.] The Significance of the Correlation Coefficient, etc. 473 
XXXIV. — The Significance of the Correlation Coefficient when ap- 
plied to Mendelian Distributions. By John Brownlee, M.D., D.Sc. 
(MS. received February 22, 1910. Bead January 24, 1910.) 
1. At the present moment there is much discussion regarding the 
means by which properties are hereditarily transmitted from a parent 
organism to its offspring, and of the extent to which the Mendelian theory 
is capable of accounting for the facts. In this note it is not proposed to 
discuss the general question hut to investigate the conditions under which 
the theory of correlation may be applied to Mendelian groupings. Two 
important papers on this subject have already been published : one by Pro- 
fessor Pearson, entitled “ A Generalized Theory of Mendelian Inheritance ” ; * 
the other, which is largely a criticism of this, by Professor Udny Yule.f In 
Professor Pearson’s paper the results produced when two organisms with 
any number of pairs of different zygotes mate indiscriminately are fully 
considered. He finds that such a population once established is stable, and 
he then deduces the parental and fraternal correlation coefficients. He 
finds that the parental correlations are independent of the number of 
zygotes, and also that the coefficients are considerably inferior in value 
to the numbers actually found by observation. Professor Yule, in criticism, 
says that the observed value of the coefficients can be obtained if a certain 
amount of weight is given to the effect of the hybrid and recessive elements, 
and he gives a formula in which this result is exhibited. 
2. Professor Yule’s criticism suggests that if the Mendelian theory is 
true, great care will be required in interpreting the meaning of a correlation 
coefficient, and the purpose of this paper is to investigate how far values of 
the latter can be taken as representations of real relationships. As Professor 
Pearson has shown that the simplest Mendelian formula has the same 
regression as the more complex, it is unnecessary for me to repeat his 
mathematical proofs, the case of the mating of two organisms differing in 
one particular giving the information required. 
3. Professor Yule has pointed out there are several varieties of corre- 
lation possible on a Mendelian basis. The chief, however, are, (1) where the 
hybrid has properties of its own differentiating it from either of its parents ; 
* Royal Soc. Trans., 1903, p. 53. 
t “ On the Theory of Inheritance of Quantitatively Compound Character on the Basis of 
Mendel’s Laws,” by G. Udny Yule. Report of Conference on Genetics, published by Royal 
Horticultural Society of London. 
