Practical implications of differing precision
INTRODUCTION
The increasing use by wool producers of diameter measurement On-Farm has highlighted the lack of information on the impact of the precision of the test result for a single sheep for sound on-farm decision-making. This fact sheet highlights the practical implications for wool growers of the differences in precision between the various technologies available to them. The information in this fact sheet is derived from a mathematical model, which enabled the TRUE diameter rank of any animal to be known.
THE IMPACT OF PRECISION ON SHEEP SELECTION
In the illustrations below the sheep in a mob of 2000 are listed in order from the finest to the coarsest. The finest is allocated a number (rank) one and the rest numbered in order up to 2000 for the coarsest. The impact of the precision of the test results can be shown by comparing the rank of each sheep based on its measured value (allowing for two levels of precision) compared to the true rank.
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Comparison of Individual Sheep Ranks for a mob with a between sheep SDD of 1.0mm and two test result precisions |
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(a) ±0.4mm |
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(b) ±1.6mm |
From this illustration a number of conclusions can be drawn:
- The greatest error in ranking occurs at the average Mean Fibre Diameter (MFD) for the mob. Small differences in the measured MFD can move the rank of a given sheep over a large number of other sheep compared to both extremes, where the same difference in measurement will have a smaller impact, as there are less sheep numbers to move over. The consequences to sheep selection are minor, as it is normally at the extremes that "On-Farm" decisions are being made (eg the coarsest to cull or the finest, in the case of rams, to keep).
- The better the precision of the test result the less the errors in the ranking of the sheep.
- For any given test-result precision, the more uniform the between sheep MFD in the mob the greater the errors in the ranking of the sheep.
Sheep selection generally has the objective of achieving a genetic gain. The following table shows the effect of between sheep variation and test precision on genetic gain for MFD. Again this is based on a mathematical model, so the same reservations indicated above apply.
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The Impact of Different Test Result Confidence Limits on Genetic Gain per Annum |
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Between-Sheep SD (µm) |
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MFD for Selected Ewes (µm) |
MFD Selection Differential (µm) |
MFD for Selected Rams (µm) |
MFD Selection Differential (µm) |
Genetic Gain per Annum (µm) |
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0.4 |
18.46 |
0.54 |
16.94 |
2.06 |
0.12 |
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1.0 |
1.0 |
18.54 |
0.46 |
17.09 |
1.91 |
0.11 |
|
|
1.6 |
18.59 |
0.41 |
17.40 |
1.60 |
0.10 |
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|
2.0 |
18.62 |
0.38 |
17.50 |
1.50 |
0.09 |
|
|
|
0.4 |
18.21 |
0.79 |
15.89 |
3.11 |
0.19 |
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1.5 |
1.0 |
18.20 |
0.80 |
15.97 |
3.03 |
0.18 |
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|
1.6 |
18.29 |
0.71 |
16.36 |
2.64 |
0.16 |
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2.0 |
18.34 |
0.66 |
16.44 |
2.56 |
0.15 |
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|
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0.4 |
17.98 |
1.02 |
15.02 |
3.98 |
0.24 |
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2.0 |
1.0 |
18.00 |
1.00 |
15.18 |
3.82 |
0.23 |
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1.6 |
18.09 |
0.91 |
15.30 |
3.70 |
0.22 |
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2.0 |
18.13 |
0.87 |
15.46 |
3.54 |
0.21 |
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The precision of the test result has a small impact on the "genetic gain per annum" in absolute terms. Putting this in context with the precision data shown in Part 3 it would appear that the current measurement systems are able to offer similar levels of cumulative genetic gain in fibre diameter over time.
THE IMPACT OF TEST RESULT PRECISION ON FLEECE CLASSING
The impact of precision on classing fleeces into different diameter classes in preparation for sale is illustrated below for a Mob with an overall average Mean Fibre Diameter of 19.0µm and a Standard Deviation of Mean Fibre Diameter between sheep of 1.5µm. A test precision of ±1.0µm was used for the purpose of setting the limits.
The sheep have been classed based on their "True Value" and their measured values based on two different Confidence Limits (±0.4µm and ±1.6µm). The tables show the comparisons of the expected Mean Fibre Diameters of the classed lines based on the average of the measured values for each fleece classed into a particular line and the average of the true values for the same fleece.
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Expected Diameters of Classed Lines Based on a Measurement Precision of ±0.4 microns |
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Expected Value |
True Value |
Difference |
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Line 1 |
17.27 |
17.30 |
0.03 |
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Line 2 |
19.06 |
19.06 |
0.00 |
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Line 3 |
20.35 |
20.32 |
-0.03 |
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Line 4 |
21.52 |
21.48 |
-0.04 |
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Expected Diameters of Classed Lines Based on a Measurement Precision of ±1.6 microns |
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Expected Value |
True Value |
Difference |
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|
Line 1 |
17.13 |
17.60 |
0.47 |
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Line 2 |
19.12 |
19.08 |
-0.04 |
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Line 3 |
20.37 |
20.06 |
-0.31 |
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Line 4 |
21.70 |
21.08 |
-0.62 |
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The difference between the "Expected Value" and the "True Value" was greatest for the finest and coarsest lines. The smaller differences are for the test procedure with the highest precision (lowest confidence limit).
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FURTHER INFORMATION
Ian Ashman
General Manager Customer Relations
AWTA Ltd
Ph: 03 9371 4103
Fax: 03 9371 4191
Email: ian.ashman@awta.com.au