The Change of Milk Flow With Age 147 



Since these tests are arranged in the book alphabetically 

 according- to the names of the sires they give no comprehensive 

 idea concerning the degree of relationship between the attributes 

 age and weekly milk production. They were hence rearranged 

 or classified in a table of double-entry or correlation. 



In the arrangement of the table, age was chosen as ordinate 

 and production as abscissa. The range of production was found 

 by inspection of the data to be from 91 lbs., the record of Julia 

 Landseer A. J. C. C. 56268, to 471 lbs. the record of Jimp A. J. 

 C. C. 86488, or a range of 380 lbs. Obviously this is too large 

 a range on which to use as a class unit a production of 1 lb., so 

 15 lbs. was chosen as this unit. For similar reasons as the range 

 of age was from 1 year 4 months, the age for the test of Alexea 

 Riotress King A. J. C. C. 176723 to 18 years 6 months, the age 

 for the test of Jersey A. J. C. C. 3260, a class unit of 6 months 

 was taken for the grouping of the cows — the first group being 

 from 1 year to less than 1 year 6 months, etc., to 18 years 6 

 months and less than 19 years, or a total of 36 intervals. 



The resulting correlation table is exhibited in Table 1. 



By observation it is easily seen that there is a distinct vari- 

 ation in production with changing age. The correlation coeffi- 

 cient in this case is r = .1925 ±: .0085. 



In view of the extreme skewness of the regression in this 

 case, as will presently appear, no particular significance attaches 

 to the correlation coefficient as such. Inasmuch as we are in- 

 terested in the present connection only with the form of the 

 regression curve we shall not develop further the purely corre- 

 lational side of the matter. 



The next step is to determine the curve of mean production 

 with changing age. This was done by first plotting as one 

 coordinate the mid-point of each age array, and as the other 

 coordinate the mean production of the corresponding array. 

 The resulting line is shown in Fissure 7. 



