8o Journal of Agricultural Research voi. xvi.no.s 



MATERIAL AND METHODS 



The Holstein-Friesian Association (75)^ has, as part of its semiofficial 

 advanced registry work, collected a considerable amount of data on the 

 yearly production of Holstein-Friesian cows. The majority of these 

 records contain the following data: The name, advanced registry num- 

 ber, and herd-book number are given, together with the volume where 

 the last entry record was made, as the requirements of the semiofficial 

 test include the making of the 7-day official test. The rest of the ani- 

 mal's record includes age at calving, length of record, weight of milk, 

 percentage of butter fat and total weight of butter. Some of these 

 records, fewer than we could desire but still far more ample than those 

 of any other known breed, give the total solids for the milk produced. 

 These records will furnish the material for the analyses of the problems 

 previously indicated. 



The objection may be raised that these data are not accurate, since 

 they are taken from this type of record. It is realized that there may 

 be some justice in the criticism; yet the inaccuracy should not be magni- 

 fied. Any advanced registry system must be subject to all the criticism 

 that may be brought against these particular records. Criticism can not 

 be made on the ground of conscious inaccuracy due to poor management 

 on the part of the association officials, as every record is carefully checked 

 for inaccuracies. Each record is under oath as to its accuracy by both 

 parties, the tester, and the owner. The only justifiable criticisms which 

 can be brought are those of the personal equation type, errors from the 

 variation in the values as read by two different men. These errors can 

 not at any time be very great. They constitute that group of errors 

 which are as likely to go one way as another — that is, they should counter- 

 balance. 



The methods used are, in general, those of any adequate statistical 

 treatment of a quantitative subject. The constants for the distribu- 

 tions, means, standard deviations, and coefficients of variations are cal- 

 culated by the usual formula for grouped distributions and without the 

 use of Sheppard (27) correction. The correlations are calculated from 

 the correlation surfaces by the usual Bravais formula. The necessity ot 

 correcting for the effect of age and quantity of milk in the comparison 

 with the amount of butter fat and solids-not-fat have made necessary 

 the use of partial correlation coefficient to measure such association for a 

 constant value of the disturbing variables. These constants have been 

 calculated from the ordinary correlations, by the method devised by 

 Pearson {21). 



VARIATION OF MILK, BUTTER FAT, AND SOLIDS-NOT-FAT 



Some study of the variation of the milk and butter fat have been 

 made, notably those by Gavin (jj), Vigor {34), and Pearl {20), where 

 definite variation constants have been determined. These studies in- 



' Reference is made by number (italic) to "Literature cited", p. 99-102. 



