H. L. RiETZ 
107 
Register, but also to the fact that there are certain entrance requirements to be 
satisfied. If we had records of all the offspring of certain grandparents with 
records, we should doubtless find many of the offspring not eligible to the Advanced 
Register for the latter reason. 
(2) Requi7'enients for Admission to Advanced Registry. 
The minimum requirements of butter fat production to admit a cow to entry 
in the Advanced Register are as follows : 
If a cow calves at two years old or under, 7"2 lbs. of butter fat in seven con- 
secutive days. If the cow calves at three years old, 8"8 lbs. fat in seven consecutive 
days. If the cow calves at four years old, 10'4 lbs. fat in seven consecutive days. 
If the cow calves at five years old or over, 12 lbs. fat are required in seven consecu- 
tive days. If the cow calves between two and three years, or between three and 
four years, or between four and five years old, every day of increased age adds to 
the requirements for the years 0'004391b. butter fat. 
Our data are therefore not a random sample of pure bred Holstein-Friesian 
cows, but a selected group which meets certain requirements. Since ancestors as 
- well as offspring must meet these minimal requirements, our problem presents an 
illustration of the double selection recently dealt with by Pearson*. A correction 
for the influence of selection will be applied (§ 9) after we obtain statistical con- 
stants from the selected groups given in the register. 
(3) Correlation of Age and Production (Table I.). 
Anticipating a high correlation between age and production, we first took the 
year books 1902 — 1906 from which can be obtained easily data necessary to 
determine the correlation between age and production. From the means of arrays 
in Table I., it follows that up to five years old, the regression is almost " truly 
linear," and that, by dividing the table into two parts, near the five year mark, 
it gives two tables of nearly linear regression in each. For this reason, we attempt 
to describe the population by separating the data into two parts at the 4'75 year 
point. It results that, for the group of cows under 4'75 years old, the correlation 
coefficient is 
r = 0-662 ± 0-007. 
For the group of cows over 4*75 years old, 
rz- 0-030 ±0-016 
if the fifteen most extreme variates with respect to age are excluded from the 
calculation. If these fifteen are included 
r = 0-004 ±0-026. 
From these results, we are able to assert a high correlation between age and 
production up to 4-75 years, but we are unable to assert that any correlation exists 
between age and production of cows over 4-75 years old. 
* Biometrika, Vol. vi.. Part i., pp. Ill, 112. 
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