CORRELATION BETWEEN THE PERCENTAGE OF FAT 
IN COW'S MILK AND THE YIELD ^ 
By Elmer Roberts 
Instructor and First Assistant in Genetics, Agricultural Experiment Station, University 
of Illinois 
INTRODUCTION 
It is a generally accepted opinion that cows with a large yield of 
milk produce a smaller percentage of fat than do cows with a small yield 
of milk. Stated in another way, it is thought that low-yielding cows 
produce a higher percentage of fat than that produced by high-yielding 
cows. 
To what extent this is true or not true has not up to the present time 
been demonstrated by a careful statistical investigation. Wilson ^ from 
a study of the records of 2,866 Ayrshire cows concluded that quantity 
and quality (yield of milk and percentage of fat) were independent of 
each other. He states: 
If we group together all the low-yielding cows, and find their milk invariably high 
in quality, we may infer that low yield and high quality are of the nature of concomi- 
tant variations. If we group the high-yielding cows together, and find their milk 
invariably of low quality, we may infer that high yield and low quality run together. 
But if we take these groups and any other groups we can form, and find that the 
quality varies the same way in them all — that is that there are low qualities, high 
qualities, and medium qualities in every one of them — ^then we are justified in inferring 
that the quantity and quality of the milk are independent of each other. And this 
is what we do find. 
In a criticism of this work Pearson,^ by means of a correlation table, 
showed that there was a small but significant decrease in the percentage 
of fat with an increase in the yield of milk, and pointed out the fallacy of 
such a process of reasoning in connection with statistical data. 
' Paper No. 5 from the Laboratory of Genetics, Agricultural Experiment Station of the University 
oi Illinois. 
'Wilson, James, the separate inheritance of quantity and QUAtriY in cows' muk. In Sci. 
Proc. Roy. Dublin Soc, n. s., v. 12, no. 3,?, p. 470-479, 6 diagr. 1910. 
» Pearson, Karl, note on the separate inheritancb op quantity and quality in cows' milk. 
In Biometrika, v. 7, No. 4, p. 548-550. 1910. 
Journal of Agricultural Research, 
Washington, D, C. 
oh 
(67) 
Vol. XIV, No. a 
July 8, 191S 
Key No. IU.-7 
