118
Sire Index for Milk Production in Cattle
ber of days of the first lactation of mothers and
daughters—sired by the bull. Of these, the
lactation records of daughters of the 5th, 9th
and the 16th pairs and of the mother of the 8th
pair are abnormal for reasons mentioned in the
remarks column, and are, therefore, omitted
from the calculations. In the remaining records
of mothers, there is none that is, either excep-
tionally high, or low, which can be regarded as
incompatible with the homogeneity of the
group. Columns 6 and 7 show the yields of
mothers and daughters adjusted to the standard
length of 300 days by the methods illustrated
in Tables II and III.
Column 8 shows the
differences between twice the adjusted yield of
daughters and the adjusted yield of mothers.
Column 9 shows the squares of the figures in
col. 8. The mean value of figures of column 8
is the Intermediate Index adjusted to the stand-
ard length of 300 days. In practice, it is not
necessary to carry out the calculations to the
last unit as shown in the table. The calcula-
tions can be simplified by rounding the figures
in the 8th column to the nearest tens.
From the sum of the 9th column is substrac-
ted a figure, known as the correction factor for
the sum of squares, which is equal to the quo-
tient of the square of the total of column 8 by
the number of pairs used. The figure so derived
is called the corrected sum of squares.
The
corrected sum of the squares divided by the
product of the number of pairs used with the
number of these pairs less one is the sampling
variance of the Intermediate Index. The square
root of the sampling variance is the standard
error of the index. As the 10 percent value of t
corresponding to the number of pairs less one is
1.796, the extent to which the calculated index
is likely to vary on either side of its value is
given by the product of the standard error and
1.796 and is shown in the last row of the table
under column 9.
TABLE I
Showing the calculation of the Intermediate Index for milk production of Sindhi Bull No. 38 from
Hosur Cattle Farm, Madras
No.
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Total
Average
Milk yield in lb.
Mothers
2
2631
3454
2034
3760
4191
3537
4810
1902
3217
4115
4297
3765
4972
3662
3586
5343
44623
3718.6
Daughters
3
3090
3149
2941
3645
931
4967
5241
5290
854
4474
4904
5313
4158
4966
3838
1492
50731
4227.6
Days of Lactation
Mothers
4
346
349
271
376
343
324
385
173†
332
349
391
339
340
374
362
384
4206
350.5
Daughters
5
262
329
280
372
87*
373
385
372
127†
361
353
374
317
382
293
207‡
4081
340.1
Adjusted yields in lb.
Mothers
(from
Table II)
6
1872
2646
2512
2506
..
3141
3408
..
..
3307
2796
3122
4312
2441
2563
..
34626
2885.5
Daughters
(from
Table III)
7
3711
2720
3268
2468
..
3774
3851
..
..
3477
4038
4103
3880
3625
3952
..
42867
3572.2
Twice
col. 7
minus
col. 6
8
5550
2794
4024
2430
..
4407
4294
..
..
3647
5280
5084
3448
4809
5341
..
51108
4259
Square
of
col. 8
9
30802500
7806436
16192576
5904900
..
19421649
18438436
..
..
13300609
27878400
25847056
11888704
23126481
28526281
..
229134028
..
Remarks
10
* Still
Birth
† Calf
Death
†Calf
Death
‡ Still
birth
Correction factor for sum of squares
Corrected sum of squares
Sampling variance of intermediate index
.....
Standard error of intermediate index
Standard error × t 10 %
(51108) 2 / 12 217668972.00
11465056.00
86856.48
294.7 lb.
529 lb.