P. V. SUKHATME
117
obviously important not to misjudge the value
of a sire by taking his calculated index at its
face value. The calculated index is only an
estimate in terms of yield of milk of the true
breeding worth for milk production of a sire.
It is, therefore, imperative to know the mag
nitude of the sampling error, so that a breeder
may know the extent to which the index is
likely to vary from chance causes.
The sampling error is measured by what is
known as the standard error in statistics, and is
calculated in the manner illustrated in the
examples given below. It is usual to add and
to substract from the calculated value of the
index a fixed multiple of the standard error to
know the extent to which the index is likely to
vary due to chance. This multiple is given by
the value of Fisher's t corresponding to the
number of pairs less one or used in calculating the
index. By convention Fisher's t at the 5
per cent. level of probability is used as multiple.
In breeding problems, however, it seems appro-
priate to use the 10 per cent level of probability
since by continuous selection the genetic vari-
ance is reduced to a level at which genetic
differences become difficult to detect.
It
is as important not to underrate the value of
a sire as it is important not to overestimate it;
and it would, therefore, seem that 10 per cent
is the most suitable level. The table below
shows the 10 per cent values of t taken from
Fisher's book on 'Statistical Methods for Re-
search Workers' and is reproduced for ready use
by breeders.
n =
10% =
n=
10% =
1
6314
16
1.746
2
2.920
17
1.740
3
2.353
18
1.734
4
2.132
19
1.729
5
2.015
20
1.725
6
1.943
21
1.721
V
1.895
22
1.717
8
1.860
23
1.714
9
1.833
24
1.711
10
1.812
25
1.708
11
1.796
26
1.706
12
1.782
27
1.703
13
1.771
28
1.701
14
1.761
29
1.699
15
1.753
80
1.697
As to how many dam-daughter pairs are
necessary to prove a sire, the answer depends
upon how sure of his proof one wants to be and
how much can be gained by testing more
daughters. If the systematic differences bet-
ween the environments of dams and daughters
are large, even after carrying out all the sug-
gested adjustments, the accuracy of the sire
index will remain low under any circumstances
howsoever large the number of dam-daughter
pairs may be.
On the other hand, if the en-
vironmental differences between dams and dau-
ghters are correctly discounted, the sire index
may be considerably increased in accuracy by
increasing the number of dam-daughter pairs.
It will thus be seen that it is difficult to fix the
minimum number of dam-daughters pairs requi-
red for calculating the index. The number of
dam-daughter pairs as recommended by differ-
ent workers varies widely. While there is no
harm in using as low a number of pairs as two
or three for deriving an indication of the breed-
ing worth of a sire, it seems undesirable to
publish an index based on fewer than six pairs,
The concept of sampling error is applicable
to a group of records which can be adequately
expressed by means of their average and the
degree of variability around it. When we say
that dams on a farm are of a particular level, we
imply this condition. Consequently, it is im-
portant to make a statistical test of signifi-
cance to cull out extreme records which cannot
be regarded without hesitation, as random
members of the group. Such a test is valid only
after the records are adjusted to environmental
differences and is justified only on the mothers'
records since an exceptional record in daughters
may result from the sampling nature of inheri-
tance. It is, however, beyond the scope of
this note to describe this test for the rejection
of extreme records.
The detailed procedure of calculating the
Intermediate Index is explained below on the
records of Sindhi bull No. 38 from Hosur Cattle
Farm, Madras. Table I shows the main steps
involved in the calculations of the index.
Columns 2, 3, 4 and 5 of the table show the
milk yield records with the corresponding num-