INSTITUTE OF AGRICULTURAL RESEARCH
ADDIS ABABA
TECHNICAL NOTE
A NOTE ON THE PRECISION OF MILK YIELD AND
BUTTERFAT MEASUREMENTS AT BAKO STATION
by
Christian Strutz
FAO, Associate Expert Animal Breeding
Bako Research Station
INTRODUCTION
This paper deals with the influence of the number of measurements on the accuracy of milk yield and butterfat percentage determinations of F1 crossbred cows at Bako Station, where a part of the Ethiopian Crossbreeding programme is carried out (Wiener; 1972, 1975). The analyses were necessary to quantify the reliability of the results obtained and to adopt a reasonable recording scheme without essential loss of information.
MATERIAL AND METHODS
Station: The environmental conditions at Bako Station have been described elsewhere (IAR, 1976).
Animals: Milk yield and butterfat determinations were made from 48 F1 crossbred cows in their first lactation. The cows are the progeny of Friesian, Jersey and Simmental sires and of Boran and Horro dams.
Records: Data of daily recorded morning (AM) and evening (PM) milk yields from Nov. 1976 to Oct. 1977 were analysed of which the records of one month of 12 cows were used for determinations of repeatability coefficients. The cows were handmilked between 6 and 8 a.m. and between 3:30 and 5:30 p.m. The individual yields were approximated to the nearest 1/10 kg. Butterfat percentage was determined as averages of duplicate measurements according to the Gerbermethod. Standardized equipment and chemicals were used as described by Ling (1963) and Kotterer and Munch (1972).
Coefficient of repeatability: The following theoretical outline is based on the lecturemanuscript of Fewson (1965). A numerical example is given in the appendix of this paper.
It is well known that by increasing the number of repetitions of measurements on a quantitative variable in the same animal, the figures tend to ‘average out’ and approach a ‘true value’ as the importance of single measurement deviations diminishes.
An estimate of the relative accuracy of repeated measurements is given by the coefficient of repeatability (0 < CR < 1),
which is defined by the formula:
where 
The estimation of the variance components is based on the analysis of variance (ANOVA) according to the model
This model applies to (n) daily milk records of (a) cows. The total number of measurements is N = n a
The structure of the analysis of variance is shown below.
Source of Variation 
Degrees of Freedom 
Sums of Squares 
Mean Squares 
Expected Mean Squares (EMS) 
Between Animals 
a  1 
SS(A) 
MS(A) 

Residue 
N  a 
SS(R) 
MS(R) 

Total 
N  1 
SS(T) 


The variance components of the sample are estimated from the expected mean squares (EMS) by
For one measurement per animal, the formula of the coefficient or repeatability (CR) represents the intraclass correlation thus giving a starting point. With more than one measurement per animal the formula shows how the magnitude of the coefficient of repeatability depends on the number of repeated measurements per animal.
Inversely, for a necessary magnitude of repeatability, the number of measurements required can be determined by
Expressed as a percentage of One, the desirable area of repeatability may be defined as that above 90 percent. The increase of accuracy by one additional measurement can then be estimated by the slope b of the repeatability curve at a given CRlevel. In mathematical terms, the first derivative at a given point of the original function yields the slope of the tangent at this point of the curve.
Transforming the formula, one can determine a target slope i.e. an increment in accuracy below which an additional measurement is not worthwhile, and calculate the necessary measurements per animal.
This method is justified if the costs  including time  of data recording and evaluation are known and a costbenefit relation between inputs and output of information can be established.
RESULTS AND DISCUSSION
The Table 1 shows the means of morning, evening and daily milk yields in 12 crossbred cows as well as the mean butterfat percentage per kilogramme whole milk in 45 cows.
TABLE 1
Means and Variance Components of Morning, Evening, Daily Milk Yield
as well as Butterfat Percentage
Item 
No. 
Measurement per 

Variance between 
Components % 
F 
Residual Standard 
Cows 
Cow 
Mean 
Cows 
Cows 
Value 
Deviation 

Milk Yield kg 







Morning 
12 
30 
4.35 
63.8 
36.2 
53.9 
0.638 
Evening 
12 
30 
2.95 
51.9 
48.1 
33.6 
0.619 
Day 
12 
30 
7.30 
74.2 
25.8 
87.2 
0.838 
Butterfat % 
45 
2 
4.75 
96.4 
3.6 
55.2 
0.164 
The throughout highly significant Fvalues being the quotients between the meansquare of the betweencow effect and the residue (MS(A)/MS(R)) at an error probability of less than one percent (p < 0.01) indicates that the cows exhibit highly distinguishable levels in their milk yield. This is especially true for the daily milk i.e. morning plus evening milk and the butterfat content.
The Table 1 also contains the residual standard deviations. They represent the square roots of the error variances which are interpreted as experimental errors (Fewson, 1965). The variance components ‘Between Cows’ and ‘Within Cows’ are the basis for the calculation of the coefficients of repeatability (CR) as shown in Figure 1.
The declining slopes of the repeatability curves are subject to the MitscherlichSpillman law of diminishing returns, where ‘returns’ are expressed as an increase of accuracy of measurements, i.e. as an increase of information. The Figure 1 shows that 3, 5 and about 8 milk recordings per cow are required for daily, morning and evening milk production respectively to reach a repeatability level of 90 percent. These results show that daily milk records comprising morning plus evening yields excel separate morning and evening milk assessments in terms of reliability. It is, therefore, suggested that combined daily milk production data should be recorded generally.
The repeatability function of the butterfat percentage with ist initial point of 96.4 percent only shows a slight curvature and inclines to 99.9 percent at 30 measurements per animal. It can be anticipated from these results that an increase of more than 2 measurements per cow and month would yield only a negligible improvement of of the very high accuracy.
In general, an increase in relative accuracy of less than two percent at a level of more than 90 percent repeatability does not seem to be justified. The coordinates at this slope are 3.8 measurements at a repeatability of 92 percent for daily milk and 1.3 measurements at a repeatability of 97 percent for butterfat determination.
Figure 1
This means in practise, that four daily milk records, i.e. one weekly, and one duplicate milk fat assessment per month are considered to be sufficiently precise and adapted to the specific variation found in the cattle herd at Bako Station. Any additional measurements would yield only marginal increases of reliability, whereas the expansion of data recorded would also increase the probability of transcription errors.
This proposal contrasts with that of Lindström (1976) who suggested a countrywide milk recording scheme for Kenya of either AM or PM milk at 14 days’ intervals. However, the statistical approach leading to this suggestion  correlations between partial and total milk yields  and the large body of data considerably differ from the method presented here.
APPENDIX
Numerical Example for the Calculation of the Coefficient of Repeatability
Four cows (a), Almaz (A), Bebaynesh (B), Chabtu (C) and Denkenesh (D) are milked for four (n) consecutive days. Their daily milk records are shown below.
Cow 
A 
B 
C 
D 

Day 





1st 
3 
4 
10 
9 
a=4 
2nd 
2 
6 
12 
7 
n=4 
3rd 
3 
5 
13 
8 
N=16 
4th 
1 
4 
12 
8 







Total 
9 
19 
47 
32= S_{xj} 
X..=107 
Mean 
2.25 
4.75 
11.75 
8.00 

1. Analysis of Variance (ANOVA)
These results are summarized in the following table.
Source of Variation 
Degrees of Freedom 
Sums of Squares 
Mean Squares 
F Value 
Between Cows 
3 
203.19 
67.73 
66.402 
Residue 
12 
12.25 
1.02 

Total 

15 
215.44 

2. Estimation of variance components
Expected mean square for MS(R)
Expected mean square for MS(A)
3. Calculation of the coefficient of repeatability (CR)
one measurement per cow:
four measurements per cow:
4. First derivative of the CRfunction showing the slope at a given number of measurements
Dr. Christian Strutz, Steigstr. 26 D88131 LINDAU
Lindau, März 1999
Homepage Dr.Christian Strutz
Über Fragen und Kritik freut sich der Autor : email Strutz_Christian@tonline.de
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