TRANSMITTING ABILITY OP HOLSTEIN-FRIESIAN SIRES 21 
bred will be prepotent. It is more difficult to judge the transmitting 
power of the dams, because of their limited number of offspring, and 
also because very often many of the offspring will be by one sire. 
On the other hand, the sire has a considerable number of offspring, 
usually from different dams, so that his transmitting ability can be 
more accurately gauged. 
A sire's transmitting ability is determined by the chance inherit- 
ance of factors governing production, which he received at the time 
of his conception. Should he by chance have received all his in- 
heritance governing production from some of his ancestry which 
carried only factors for low production, then he will transmit only 
low production to his offspring, regardless of how man}?- high-produc- 
ing ancestors he may have. 
Once a bull has proved himself to be a poor sire it would seem that 
there is little chance of his transmitting any of the ability of his more 
worthy ancestors. 
WHICH PARENT HAS THE GREATER INFLUENCE ON MILK YIELD, 
BUTTERFAT PERCENTAGE, AND BUTTERFAT YIELD? 
A study was made of the correlation between the daughters and 
their dams, with respect to total yield of butterfat, for each of 23 
sires having 6 or more tested daughters from tested dams. The 
results of this study are shown in Table 10. The correlation coeffi- 
cients range from —0.39 for sire N to +0.90 for sire P. 4 
* Perhaps a brief explanation of the meaning of correlation should be made before discussing Table 101 
A correlation coefficient shows to what extent the variation in one character follows or is coordinated with 
the variation in some other character. For example, many are of the opinion that in order to get high 
production in dairy cows we must have large cows If this assumption is true, then there should be a 
positive correlation with respect to production and size. If milk and butterfat were produced more eco- 
nomically with small cows then there would be a negative correlation with respect to economical production 
and size. Or, a correlation coefficient may indicate to what degree the same character, such as yield of 
milk or butterfat, exists between parent and offspring; and that is the thing intended to be determined in 
this table. 
This relation of the yield of milk and butterfat between parent and daughters is expressed as a coefficient. 
If a high yield of milk or fat in the dam is followed by a correspondingly high yield in the daughter, the 
correlation would be perfect and the coefficient would be 1. If, on the other hand, the highest-yielding 
daughters all came from the lowest-yielding dams, and the lowest-yielding daughters all came from the 
highest-yielding dams, then there would be a perfect negative correlation and the coefficient would be — 1. 
Again, if there is no relation between the yield of the daughter and the yield of her dam, indicating that 
there is no correlation, then the coefficient would be 0. It is seldom that a perfect correlation is found; 
usually the correlation is between and +1, or between and — 1. 
The correlation coefficient is arrived at by a rather complicated mathematical formula. It expresses in 
mathematical terms the extent of the relation which exists between two characters, or the extent to which 
a character is common to two individuals. If the coefficient is low, it indicates that there is very little 
relation; if it is high, there is a close relationship; and if it is so high as to indicate a perfect correlation, 
then it may be said that one is probably the cause of the other. The correlation coefficient when expressed 
in writing is followed by the probable error; that is, the amount to be added to or subtracted from the 
correlation coefficient to get the two limiting figures within which there is an even chance that the true 
value will lie. 
The following rules are suggested in Babcock and Clausen (#) for the interpretation of coefficient of 
correlation: 
1. If r (the coefficient of correlation) is less than the probable error, there is no evidence whatever of 
correlation. 
2. If r is more than six times the size of the probable error, the existence of correlation is a practical 
certainty. 
3. In cases where the probable error is relatively small: 
o. If r is less than 0.3, the correlation can not be considered at all marked. 
b. If r is above 0.5, there is decided correlation. 
