In order to determine the accuracy of a specific method, I need to determine if the results are statistically precise. In the example below, I am taking a sample from 7 individuals and running their sample twice. For each row I calculated the mean SD and Coefficient of Variation. Ideally the CV should be <15%. Is it appropriate to average the CV values?

enter image description here

My question is whether or not it is acceptable to average the CV values to get one CV. Or is there another more appropriate way to approach this problem?


First, if you are working with a measurement system where you expect a constant CV over a range of necessarily positive values, then it's often best to work with logarithmically-scaled data instead of the raw values. The assumptions behind many statistical tests require that the magnitudes of residual values around mean values be independent of the magnitudes of the values themselves; roughly, the SDs should be independent of the mean values. That's not true with your data in their original scale, but if you expect constant CV among samples then it should be true on a log scale.

Second, the CV is the ratio of the SD to the Mean, and the sample SD is a biased estimator. So it would be inappropriate to average the necessarily biased CV values.

It's best to use variances rather than SDs for this type of analysis, as the variance of a sum of independent variables is the sum of their individual variances. Given your type of data, you could consider working with values transformed on a natural log scale, and then performing a simple analysis of variance (ANOVA) among the samples.

ANOVA will give a residual mean square, representing the estimated variance of observations around the corresponding sample mean values, pooled among all the samples. The square root of that residual mean square is an estimate of the SD around the mean values, and with natural-log-transformed data that square root directly provides a pooled estimate of the CV.

Note, however, that your estimate of the CV from just a few samples like this can be quite different from the true underlying CV. See this paper for the number of cases that need to be examined to obtain CV estimates with desired confidence limits.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.