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Bulletin 397 



Group variation 



In the ordinary feeding experiment, groups of cows of equal total pro- 

 duction are made up for the competitive rations. Therefore a study of 

 group variation is important. It is possible, of course, to compute the 

 probable coefficient of variability of a group of given nimibers, given the 

 coefiEicient of variability of the individuals. However, there were reasons 

 why it seemed desirable to make a statistical study of group variation. 

 In the first place, the calculated value on the basis of individual variation 

 could thus be checked up. Further, a study of group variation was found 

 to be the best method of studying the influence of various selective factors 

 considered in forming. groups. 



In most of the work on group variation the groups were made up of 

 six individuals. This was found to be the most convenient grouping 

 with the records at hand, and it represents the typical-sized lot used in 

 feeding trials. Some comparative studies were made of groups of various 

 sizes. In making up lots of equal production on the basis of the preliminary 

 period, a range of 100 pounds in the total production of the groups was 

 allowed. Some study was made, however, of the effect of varying this 

 range. 



Variation in groups of wiselected individuals. — Groups were made up 

 of individuals taken at random, the only consideration being that the 

 total production of each group for the preliminary period should fall 

 between 3200 and 3299 pounds. The results of the study of variation 

 in these groups are shown in table 2 : 



TABLE 2. Variation in Groups of Unselected Individuals 



From the results shown in table 2, it is evident that the variation of 

 groups of cows selected in this way is much less than for individuals as 

 shovni by table i . The relation of individual variation to group variation 

 is shown by the formula ;;:^ = C, in which c is the coefficient of vari- 

 ability of individuals, C the coefficient of variability of groups, and n the 

 number of individuals in a group. Using the average coefficient of 

 variability of individuals as shown in table i, and solving this equation 

 for groups of six, it is found that the coefficient of variability of a group 



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