Refinement of Feeding Experiments for Milk Production 227 



of this size would be 4.84 per cent. This computed coefficient^ checks 

 closely with the coefficient found by actually testing groups of six, as 

 shown by table 2 . 



Variation in groups of individuals of equal production. — In the pre- 

 ceding study no attention was given to the production of individuals 

 except in so far as was necessar}^ to make up groups of like production. 

 It seemed desirable to determine the effect on group variation of selecting 

 animals of equal individual production. The range allowed for indi- 

 vidual production during the two-weeks period was 50 pounds. Groups 

 of six of these equal individuals were so selected as to allow a 100-pound 

 range for the group. The results of the study of their variation are 

 shown in table 3 : 



TABLE 3. Variation in Groups of Individuals of Equal Production 



Individual production, two-weeks period 

 (pounds) 



450-499 . 

 500-549 . 

 600-649 . 



Total . . . 

 Average . 



Group production, 



two-weeks period 



(pounds) 



2 , 800-2 , 899 

 3,100-3,199 

 3 , 700-3 , 799 



Number 

 of groups 



13 



Coefficient of 

 variability 



1.90 ± 0.45 

 3.58 ± 0.76 

 3.38 ± 0.81 



3.00 ± 0.41 



It is seen from the table that the average coefficient of variability of 

 groups of like individuals is 3 .00 ± 0.41, as compared with 5 .09 ± 0.42 

 for groups of unselected individuals. The difference between these two 

 values is 2.09. In order to determine the degree of reliance that can be 

 placed on this difference, its probable error should be computed. The 

 probable error of the difference between two coefficients of variability 

 is the square root 'of the sum of the squares of the probable errors 

 of the coefficients under consideration. The probable error of the 

 difference just given is ±0.59, and the difference, with its probable 

 error, would be expressed as 2.09 z±= 0.59. If the probable error were 

 exactly as large as the difference, the chances would be even that a repe- 

 tition of the study would result in lower variation for similar individuals, 

 and likewise even that the opposite result would be obtained. The dif- 

 ference under discussion is 3 . 5 times its probable error. The odds are 



' The range of 100 pounds allowed in selecting groups of equal production is not proportional to the 

 range of 50 pounds allowed in selecting individuals of equal production. The results of studies described 

 elsewhere in this bulletin, however, indicate that such variations in the range allowed in selecting groups 

 or individuals of equal production do not have any appreciable effect on variation in milk production 

 during the experimental period. 



22 



337 



