Refinement of Feeding Experiments for Milk Production 225 



Individual variation 



The records were first di\dded into classes of individuals of uniform 

 production for two weeks, all the individuals of similar production being 

 put in the same class. The limits of each class had a range of 50 pounds, 

 these limits being 250-299, 300-349, and so on. The variation of indi- 

 viduals within these classes is shown in table i : 



TABLE I. Individual Variation 



Class production, two- weeks period 

 (pounds) 



250-299 



300-349 



350-399 



400-449 



450-499 



500-549 



550-599 



600-649 



650-699 



700-749 



750-799 



800-849 



Total 



Average* 



Number of 

 individuals 



8 

 II 

 17 

 13 



28 



31 

 20 



23 

 9 

 8 

 6 

 4 



i: 



Coeflficient of 



variability during 



eighteen- weeks 



period 



15 

 14 

 13 

 12 

 II 

 10 

 II 



74 

 66 



39 

 40 



14 

 02 



26 



± 

 ± 

 ± 



65 

 II 



55 

 64 

 ,00 



9 53 

 14.60 

 10.88 



1753 

 II .69 



±0.86 

 ± 1 .20 

 ± 0.95 

 ±2.32 

 ± 1.83 



± 3-41 

 ±2.79 



11.87 ± 0.43 



* The average coefficient here given is the weighted average of the coefficients of the different classes 

 of individuals. In spite of the recognized shortcomings of any method of averaging coefficients of vari- 

 ability, it is believed that this procedure gives a fairly trustworthy idea of the variability of the individuals 

 it represents. All average coefficients used in these studies are weighted averages. 



In order to check the accuracy of the average coefficient as the measure of individual variability of the 

 individuals here included, the coefficient of variability was computed from the weighted average standard 

 deviation and the weighted average mean of the classes in the table. This method gave a coefficient of 

 variability of 11.72 ± 0.42. The close agreement of this coefficient with the average coefficient indicates 

 the essential accuracy of the method used. 



The probable error of the average coefficient of variation is the weighted average of the individual prob- 

 able errors. It is computed by weighting each probable error, squaring these products, summing, extract- 

 ing the square root, and dividing by the number of probable errors. 



The results shown in table i indicate the approximate range of vari- 

 ability, during an experimental period of eighteen weeks, of cows of similar 

 productive capacity as indicated by their production for a trial period 

 of two weeks. The coefficients of variability range from 9.53 to 17.53 

 per cent for individuals in the different classes, the average value for the 

 178 individuals being 11.87 ±0.43 per cent. It is seen that both the 

 high producers and the low producers show a somewhat greater varia- 

 bility than the middle classes. However, no conclusion can be drawn 

 from this, because none of the differences are significant when their prob- 

 able errors are considered. 



335 



