56 PROTEIN REQUIREMENTS OF CATTLE: MITCHELL 



Concerning the homogeneity of these sets of data, it appears from the 

 distributions given in Table 28 that no distinct discrepancies exist among 

 the first four sets of data. The Jersey data, however, indicate a rather 

 distinctly lower protein content for milk containing more than 3.50 per 

 cent of fat. Since the greater discrepancies occur in those groups pos- 

 sessing the smaller numbers of samples, it appears that no serious error 

 would be committed by pooling all of the analyses together. This has 

 been done in Table 29, and the average percentages in each array have 

 been corrected to the nearest even 0.5 per cent of fat on the assumption 

 of an equal ratio of protein to fat. For example, in the array of analyses 

 from 3.26 to 3.75 per cent of fat inclusive, the actual averages of the 295 



TABLE 29 



A Comparison of Haecker's and Overman's Averages for the Protein Contents 



OF Milk of Different Fat Content and of Predicted Protein 



Percentages Derived from the Equation P = 2.0+0.4 F 



Per cent protein according to 



1 According- to Haecker: " Tliere were so few .samples containing less than 2.5 per cent of fat, 

 and so many more testing from 2.5 to 2.75, that no satisfactory average could be obtained for milk 

 testing 2.5 per cent butter fat, so the averages were computed from the ratio of variation of milk 

 testing from 3 to 3.5 per cent fat." 



analyses are 4.53 per cent of fat and 3.40 per cent of protein. The per 

 cent protein corresponding to 4.50 of fat is computed from the proportion 



4.50 _ _^ 

 4.53 ~ 3.40 ■ 

 For comparison, Haecker's analyses ' are also given in Table 29, and in 

 the last colmnn of the table will be found the results of predicting the pro- 

 tein content of milk from the fat content by the equation p = 2.0-1- 0.4 f. 



'It is a peculiar fact that, in the appendix of Haecker's bulletin containing 

 presumably the original 543 analyses of milk, the average percentages of fat in 

 each of the 9 classes are equal exactly to the mid-values of the class. If these were 

 random selections of samples, such an ideal result would be statistically impossible 

 with the small numbers of samples analyzed in each group. The obvious conclusion 

 is that some selection of data • has occurred, or that the analyses have been 

 modified in some unrevealed way, in order to secure these ideal averages. 



