Jan. 20, 1919 Variations and Mode of Secretion of Milk Solids 87 



Table VIII gives the values of the correlation coefficients and the 

 correlation ratios, together with the constants to show the approach to 

 linearity of the regression lines. 



Table VlU.~A7ialytical constants for inter-individual variation of the constituents of 



cow's milk 



Character correlated. 



Weight of milk and percentage of butter 

 fat 



Age and percentage of butter fat 



Weight of milk and percentage of solids- 

 not-fat 



Age and percentage of solids not fat with- 

 out doubtful observation 



Weight of milk and percentage of solids- 

 not-fat 



Age and percentage of solids-not-fat 



0977±o.oi56 

 0546± .0181 



05S3± -0367 

 i6l2± .0359 



0659 ± .0367 

 2I9I± .0351 



o. i25i±o.oi55 

 • I32S± .0178 



. n6i± .0364 

 . 234i± .0348 



•I373± -0362 

 . 24S9± .0347 



o. 1213 

 .1917 



•l8S7 

 • 3084 



• 2032 

 .1883 



o. 006 1 ±0. 0024 

 .oi46± .0044 



. oio4± -0075 

 . 0288it .0124 



.oi4S± .0089 

 • 0I25± .0082 



This table shows that the weight of milk produced in a year is nega- 

 tively correlated with the percentage of butter fat and of solids not fat 

 contained in this milk. In each case the correlation is low, in neither 

 case being as great as -o.i. For the butter fat percentage the corre- 

 lation- 0.0977 ±0.01 56, although low, is highly significant, since the 

 correlation value is 6.2 times its probable error; or, in other words, 

 could be expected from random sampling only once in slightly more 

 than 100,000 times. The correlation for percentage of solids not fat 

 and milk, -0.0553 ±0.0367, is only about half that for the percentage 

 of butter fat and milk. Further, this correlation can not be considered 

 significant, as it is only 1.5 times its probable error, or about once out 

 of three trials a correlation as great or greater than this due to random 

 sampling would be expected. It will be noted that even where the 

 abnormal observation is eliminated the correlation does not increase to 

 a value where it becomes significant. 



The correlation between the percentage of butter fat and age is sUght 

 (-o.0546io.0181) and in the same direction as that of butter fat and 

 milk production— that is, minus. It may possibly be significant, since 

 it is about 3.1 tiines its probable error. Even if it were significant, 

 however, it would be scarcely detectable except in a large mass of data 

 where statistical methods were applied. 



On the other hand, the correlation between age at test and percentage 

 of solids-not-fat is significant, for, with the doubtful observation, the 

 correlation is 4.4 times its probable error, and without this doubtful ob- 

 servation the correlation is 6.2 times the probable error. Furthermore, 

 the difference between the correlation of percentage of butter fat and 

 percentage of solids-not-fat in cow's milk and the age at which the test is 

 made ^ is probably a significant difference. The difference of the corre- 

 lation of the percentage solids-not-fat and age and the correlation be- 



' The probable error of the difference is calculated by the usual formula ±0.67449 Vo^H^ 



92803°— 19 2 



