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Coefficient of variationDefinition Intra-assay & inter-assay coefficients of variation Uses Assumptions & requirements
The coefficient of variation of the observations is used to describe the level of variability within a population independently of the absolute values of the observations. If absolute values are similar, populations can be compared using their standard deviations. But if they differ markedly (for example, the weights of mice and elephants), or are of different variables (for example, weight and height), then you need to use a standardized measure - such as the coefficient of variation.
The coefficient of variation (CV) for a sample is the standard deviation of the observations divided by the mean:
The estimate we get from this equation is a biased estimator of the population coefficient of variation. Hence we should use the following equation to give CVcor, which is the sample CV corrected for bias:
Note :When you use a sample standard deviation to estimate the population coefficient of variation, you should not correct the sample standard deviation for bias, as this correction is included in the equation above. It only differs slightly from the formula for correcting the standard deviation for bias.
Intra-assay and inter-assay coefficients of variation
These are frequently used by microbiologists to describe the precision of an assay (such as an ELISA) when applied to portions of the same specimen. In other words, each specimen is divided into a number of aliquots, and the set of aliquots are subject to an identical procedure - in order to measure the reliability of that procedure. Intra-assay and inter-assay precision are two distinct measures of
The most common use of the coefficient of variation is to assess the precision of a technique.
Target values for intra- and interassay coefficients of variation are generally 5% and 10% respectively. For assays conducted over long period, coefficients of 7% and 15% are more typical. If the intra-assay coefficient of variation exceeds 10% or the interassay coefficient of variation exceeds 20%, then it is time to identify the source of the variation.
Similarly, when agricultural field trials are carried out on maize, the coefficient of variation of the yield is usually between 5 and 15%. If a researcher gets a markedly larger figure than this in a yield experiment, he should investigate the
The most widely used measure of variability when the standard deviation is proportional to the mean is the standard deviation of the log transformed observations. This generally removes the dependence of the variance on the mean. But it has the disadvantage that when there are zeros in the data, one has to add a constant (usually 1) prior to taking logarithms. This results in a serious underestimate of the true value of the standard deviation.
The coefficient of variation largely overcomes these problems. It is independent of the mean, and is unaffected by zeros - although if the mean value is near zero, the coefficient of variation is unduly sensitive to small changes in the mean.
For example, in animal productivity studies one may wish to assess which of a wide range of variables (such as milk yield, time to first calving, and age at maturity) is most variable. Since these are measured in different units, the measure of variability must be standardized. The coefficient of variation achieves this by dividing the standard deviation by the mean.
Assumptions and requirements
The coefficient of variation is only applicable for measurement (continuous or discrete) variables where measurements are made on a ratio scale. In other words the scale should have a non-arbitrary zero value. It is not appropriate for variables which can take negative values. It should also only be calculated on untransformed data. For it to function as a standardized measure, the standard deviation should be directly proportional to the mean. When being used as a measure of reliability - for example if you are estimating the repeatability of measurements on different individuals - it is assumed that these measurements all vary to a similar degree after allowing for the difference between their means.