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Should alpaca breeders use ‘SD’ or ‘CV’ or both when evaluating fibre traits?

Over the years I have operated AAFT, the question of whether to use Standard Deviation (SD) or Co-efficient of variation (CV) when evaluating fibre traits is undoubtedly one of the most frequently questions asked. It also happens to be one of the issues most plagued by misunderstanding, and consequently, carries the potential to de-rail breeding strategies aimed at improving the quality of fleeces. 

One of the most useful aspects of fibre testing, is the ability to measure the degree of variation in fibre diameter. Variation in fibre diameter is correlated with processing performance of fleeces, ‘handle’ of fleeces, micron blow-out, tensile strength, variation in diameter over the fleece and incidence of coarse fibres. The major benefit in using fibre diameter variation, however, is its high level of heritability, meaning breeders are able to achieve substantial genetic gains using this trait. 

The two statistics used when measuring variation of fibre diameter are Standard Deviation (SD) and Co-efficient of variation (CV). In saying this, however, it might also be noted that fibre test histograms provide a graphical representation of fibre diameter variation. 

To determine whether to use SD or CV for the purposes of selecting breeding stock, it is appropriate to calculate SD and CV for two imaginary samples of fibers. 

While we obviously use software programs to calculate these statistics, I will do it manually. For ease of calculation, the samples will have a ridiculously small number of fibers. 

The first sample has 5 fibers, each with the following average diameter in microns: 18, 19, 19, 20 & 21. The AFD of this sample is therefore 19.4 microns

We calculate the SD as follows =

1/ obtain the sum of the squares for each of the data values (eg 324 + 361 + 361 + 400 + 441 = 1887)

2/ square the sum of the data values and divide by the number of values (eg 18 + 19 + 19 + 20 + 21 = 97, thence 97 x 97 divided by 5 = 1881.8)

3/ subtract 2/ from 1/, then divide the answer by the number of values less 1 (eg 1887 - 1881.8 = 5.2, thence 5.2 divided by 4 = 1.3)

4/ obtain the square root of 3/ (eg, the square root of 1.3 = 1.14

The SD of the sample is therefore 1.14

Now take a second sample of fibers with exactly the same degree of variation (distribution of fibers from the mean) Lets say the microns of the five fibers are 23, 24, 24, 25 & 26. (AFD of 24.4)

The calculations for SD of this second sample are:
1/ 2982
2/ 2976.8
3/ 1.3
4/ 1.14 

The SD is also 1.14. The SD is the same because they both have precisely the same degree of fibre diameter variation.

If, on the other hand, we take a sample with a higher degree of variation in the diameter of the fibres, the SD will also be higher, for example, fiber microns of 23, 24, 24, 25 & 29. (AFD of 25.0 microns)

The calculations are:

1/ 3147
2/ 3125
3/ 5.5
4/ 2.3

The SD is 2.3. 

At this point, it should be clear that SD is the true and unbiased indicator of variation. 

This then brings us to CV. We calculate CV by dividing the SD by the AFD and then multiply by 100. In other words, because of the way we calculate CV, the higher the AFD, the lower the CV. Let me give some examples.

The first sample mentioned above will have a CV of 5.9%, (1.14/19.4 x 100). The second sample has a CV of 4.7%. 

Further, lets take two alpacas with identical variation, say, SD of 4.7. One has AFD of 22.0 microns, the other is 27.0 microns. Their CV's are therefore 21.4 and 17.4.

The problem is that when breeders are selecting low CV alpacas, the alpaca may in fact have a very high variation of fibre diameter, but also have a high AFD. Using CV, therefore, can conceal the fact that an alpaca has a high number of very coarse fibers.

The message is simple. Use SD and not CV.