PROBLEM OF NURTURE AND NATURE 45 



But does any one trained in statistics believe that you add 

 correlation coefficients together to get their combined effect? 



You might as well suggest that when you combine a force of 10 Ib. 

 with a force of 10 Ib. the resultant is 20 Ib., whereas it might be 2 Ib. 

 or possibly zero. The whole relationship depends on the angle between 

 the forces. In the same way the value of the coefficient of multiple 

 correlation depends on the correlations between the combined factors. 



It is absolutely needful to impress this on the reader, and I will 

 illustrate it for a special case. Let the problem be: How far does 

 professional occupation, and prosperity influence the size of the 

 family ? 



I take for the London districts 1 the number of births per 100 wives 

 from 15 54 in a district. I take the number of professional men 

 per 1000 occupied males and the number of female domestic servants 

 per 100 females. We have: 



Correlation of births and professional men = -78 ; 

 and domestic servants = -80. 



Now suppose we wanted to find the total effect of professional 

 occupation and middle class prosperity as measured by the prevalence 

 of domestic servants on the birthrate. If you were to add -78 to 



- -80 you would get 1-58, which is senseless, for correlation cannot 

 be greater than the perfect value unity! Actually the multiple 

 correlation coefficient is -82, only -02 more than the value as found 

 for domestic servants alone and this result is as wholly reasonable as 

 the additive result was wholly fallacious. For to provide a measure 

 of the professional men in a district is almost equivalent to providing 

 a measure of the domestic servants in the same district. The correlation 

 between these two measures is in fact + -85. A knowledge of the two 

 factors does not give double information, and enable us to determine 

 double as accurately the birthrate ; it only raises the correlation from 



- -80 to - -82. 



Let us take a second illustration of this same most important 

 principle. Suppose we desire to predict the probable character of an 

 individual from (i) his two parents or from (ii) a large number of his 

 brothers and sisters. In the first case and in the second the correlation 

 between the individual and one only of his relatives is about the same, 



1 See Heron, On the Relation of Fertility in Man to Social Status, &c., Cambridge 

 University Press, Drapers' Company Research Memoirs. 



