400 
R. A. FISHER ON THE CORRELATION BETWEEN 
which obscure the essential distinction between the individual and the population, 
should be carefully avoided. 
Speaking always of normal populations, when the coefficient of correlation 
between father and son, in stature let us say, is r, it follows that for the group of 
sons of fathers of any given height the variance is a fraction, 1 — r 2 , of the variance 
of sons in general. Thus if the correlation is '5, we have accounted by reference 
to the height of the father for one quarter of the variance of the sons. For the 
remaining three quarters we must account by some other cause. If the two parents 
are independent, a second quarter may be ascribed to the mother. If father and 
mother, as usually happens, are positively correlated, a less amount must be added 
to obtain the joint contribution of the two parents, since some of the mother’s 
contribution will in this case have been already included with the father’s. In a 
similar way each of the ancestors makes an independent contribution, but the total 
amount of variance, to be ascribed to the measurements of ancestors, including 
parents, cannot greatly exceed one half of the total. We may know this by 
considering the difference between brothers of the same fraternity : of these the 
whole ancestry is identical, so that we may expect them to resemble one another 
rather more than persons whose ancestry, identical in respect of height, consists 
of different persons. For stature the coefficient of correlation between brothers is 
about ‘54, which we may interpret* by saying that 54 per cent, of their variance 
is accounted for by ancestry alone, and that 46 per cent, must have some other 
explanation. 
It is not sufficient to ascribe this last residue to the effects of environment. 
Numerous investigations by Gr Alton and Pearson have shown that all measurable 
environment has much less effect on such measurements as stature. Further, the 
facts collected by G Alton respecting identical twins show that in this case, where 
the essential nature is the same, the variance is far less. The simplest hypothesis, 
and the one which we shall examine, is that such features as stature are determined 
by a large number of Mendelian factors, and that the large variance among children 
of the same parents is due to the segregation of those factors in respect to which 
the parents are heterozygous. Upon this hypothesis we will attempt to determine 
how much more of the variance, in different measurable features, beyond that which, 
is indicated by the fraternal correlation, is due to innate and heritable factors. 
In 1903 Karl Pearson devoted to a first examination of this hypothesis the 
* The correlation is determined from the measiireinents of n individuals, x v x 2 , . . . x n , and of their brothers, 
y v y 2 , . . ., y r ; let us suppose that each pair of brothers is a random- sample of two from an infinite fraternity, that 
is to say from all the sons which a pair of parents might conceivably have produced, and that the variance of each 
such fraternity is V, while that of the sons in general is <r. Then the mean value of (x — y) 2 will he 2 V, since each 
brother contributes the variance V. But expanding the expression, we find the mean value of both x 2 and y 2 is <r 2 , 
V 
while that of xy is ra 2 , where r is the fraternal correlation. Hence 2V=2<r 2 (l — r), or ^=1 -r. Taking the values 
•5066 and - 2804 for the parental and marital correlations, we find that the heights of the parents alone account for 
40T0 per cent, of the variance of the children, whereas the total effect of ancestry, deduced from the fraternal 
correlation, is 54'33 per cent. 
