550 
Miscellanea 
How now doefs Professor Wilson extract from these data the independence of quality and 
quantity of rnilk on which he insists, and which is chosen as the very title of his paper ? He 
has prepared six elaborate diagrams, and he leaves the reader from mere inspection of these to 
come to the same conclusion as himself, i.e. that the variation is the same in all his groups and 
the quality independent of the quantitj'. Not being able myself to judge from such diagrams 
whether there is complete independence between quality and quantity, I thought it worth while 
to ascertain the mean percentages of fat and the variations in fat of his four groups. The results 
ai'e as follows, the probable errors being added : 
Quantity of Milk 
Means 
Standard Deviations 
Under 500 gallons 
From 500 to 600 gallons ... 
From 600 to 700 gallons ... 
Over 700 gallons 
3-710+ -010 
3-673+ -007 
3-651+ -008 
3-640± -008 
•372+ -007 
•319+ -005 
•321 + -005 
•275+ -006 
Tlic means and variabilities are in percentage of butter-fat. 
For tlic wliole population of 2866 cows the mean is 3-672 and the variability is measured by 
3'230. It will accordingly be clear that there is (i) a slight but perfectly definite decrease in 
quality with increase of quantity, the low-yielding cows have a higher, the high-yielding cows a 
lesser fat percentage than the average Ayrshire, althougli the increase and decrease only amount 
to about 1 °/„ of the average yield, and (ii) the variation in quality is not the same for cows of 
each quantity category. Cows which give high quantity have far less variation in their yield of 
butter-fat than cows of low yield. The number of cows is so large relatively that the probable 
errors are small and there is no doubt about the results being significant. Owing to the manner 
in which the tails of the above frequency liave been clubbed together it is not possible to work 
out the ])ro])er correlation by the ordinary' product moment method. The means, however, 
suggest that the correlation cannot be very far from linear, and the correlation ratio r) may be 
fairly taken to measure r. This gives us -^075 with a probable error of ±^013, a result, 
if small, yet definitely significant. 
It seemed worth while putting these numerical results on record, as a further protest against 
somewhat dogmatic inferences drawn from mere inspection of elaborate but unnecessary graphs. 
CAMlililDGE : PRINTED BY JOHN CLAY, M.A. AT THE UNIVEKSITY PRESS 
