Essay on the Interpretation of Milk Records. 155 



lactation, was perhaps unduly liable to error, as such variations 

 as those caused by late milking, early milking the previous 

 afternoon, extra food, and clerical mistakes, would have full 

 weight. The work was therefore repeated and a third figure 

 considered, namely : — 



3. Maximum daily yield maintained or exceeded for not 

 less than three entries in record book.^ 



For the sake of brevity these three figures are called 

 hereafter — (1) Average, (2) Maximum, and (3) Revised Maxi- 

 mum, or R.M. 



Now taking the disturbing factors in detail, these measures 

 will all presumably be fully influenced by (1) the age of cow ; 

 but (2) the number of weeks in milk will have no effect ; and 

 they should also be outside the influence of (4) interval 

 between calving and subsequent service. 



This leaves factors (1) age, (2) length of " rest " before 

 calving, and (5) season of year of calving to be considered. 

 Food, weather, and general treatment have not been statistically 

 dealt with. 



By using any of these figures, then, for describing a cow's 

 capabilities, we at once eliminate two of the most powerful 

 exterior causes of variation, and if this idea be pursued further 

 it seems probable that the most accurate indication of this 

 character of giving milk must be rendered by that function 

 of the yield which shows the least variability. 



The variabilities of the three suggested figures have there- 

 fore been calculated and compared with one another and 

 with the variability of lactation totals, the latter having 

 been chosen as being the most reasonable of the ordinary 

 standards of measurement. Comparisons have been made by 

 means of the " coefficient of variability " (v)" which is simply 



100 X standard deviation / 100 o-\ , / 2 d^ / 



~~~ mean \ M /' '^ "■ — y — ^ - 



i.e. the square root of the sum of the products of each frequency 

 and its squared deviation from the mean, divided by the total 

 number of variates. There is thus obtained a series of abstract 

 expressions of variability comparable with one another and 

 dependent neither on measurements adopted, as is the standard 



1 In the records on which this work is based the yield of cows is recorded 

 weekly, but where it is the practice to record daily, the R.M. would be taken 

 from three daily entries. 



The three highest daily yields (whether entered weekly or daily) «are first 

 noted. Four cows, for example, might give 16, 16, 16—16, 17, 17—16, 18, 16— 

 16, 17, 18 quarts. The R.M. is then taken as the highest yield common to the 

 three entries. Thus, in all the four cases quoted it would be 16 quarts. 



■^ Karl Pearson : "Regression, Heredity and Panmixia," Phil. Trans. Roy. 

 Soc, clxxxvii., 1896, page 276. 



