224 Bulletin 397 



A range in milk production not exceeding 50 pounds for the two-weeks 

 period was the basis of selecting classes of individuals of like production 

 in most of the work. The limits, in terms of nurnber of pounds yield 

 for two weeks, were therefore as follows: 200-249, 250-299, and so on. 

 By this system the percentage of range allowed was greater with groups 

 of small production. In order to ascertain whether this variation had 

 any appreciable effect, a percentage system was used in part of the work; 

 a range of 10 per cent was allowed, and the limits became 200-2 19, 220-241, 

 and so on. 



In measuring the variation in production, during the eighteen-weeks 

 period, of individuals and of groups selected on the basis of production 

 during a preliminary period, the coefficient of variability ^ was the 

 constant employed. This constant is the standard deviation of the 

 individual production expressed as a percentage of the arithmetical mean 

 production. 



The probable error of each coefficient of variability was computed, 

 in order to have a statistical measure of its reliability. The acctu-acy 

 of a given coefficient of variability as a measure of the variation of the 

 groups or the individuals it represents, depends on the number of groups 

 or of individuals. The probable error of a given coefficient defines the 

 limits above or below the computed coefficient within which the true 

 coefficient has an even chance of falling. If the coefficient of variability 

 of the individuals in a given group is found to be 10 per cent and its 

 probable error is ± i , the chances are exactly even that the true coefficient 

 of variability of this group will fall between nine and eleven per cent. 



In the preceding paragraphs the general methods used in this work 

 are outlined. Certain other procedures have been followed in special 

 cases, accounts of which are given under the cases in question. 



STUDIES OF HOLSTEIN RECORDS: COWS IN UNIFORM STAGE OF LACTATION 



The animals used in this part of the study freshened between August 

 1 5 and December 1 5 , and the twenty-weeks period was started one month 

 after calving. The results of this selection furnish records of animals 

 uniformly advanced in their period of lactation and similar as regards 

 the season in which the twenty- weeks period was chosen. The object 

 of the study was to determine the normal range of individual and group 

 variation under these conditions, and to determine the effect of certain 

 other factors of selection on variation. 



- In this bulletin no attempt has been made to discuss the theories of the vanous statistical measure- 

 ments employed. For a full discussion of the theories of variation and probable error, the reader is referred 

 to the following standard works on statistics: Statistical Methods (1914), by C. B. Davenport; An Intro- 

 duction to the Theory of Statistics (1912), by G. U. Yule. 



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