I am trying to compare test measurements taken at three time points in a training paradigm. The data for each test consists of a number of durations in ms. The variable I'm interested in is the coefficient of variation (or CV, i.e. the standard deviation as a percentage of the mean), so the extent to which all the durations within that test are the same. My hypothesis is that this variation will decrease over time due to training as responses become more regular.

However, the training also results in more data points being collected in the 3rd test as compared to the first (varying from about 40 data points to 140 in some cases), leading to a decrease in standard deviation that has nothing to do with the training or a potential increase in regularity of the responses.

The question I have is whether anyone knows of a way to correct for sample size when estimating the standard deviation, so that I can compare the CV between different tests. As the test data are (in some cases) not normally distributed, I've been looking at this page on bias correction for clues but I'm not sure that's what is needed in this case.

Any help would be much appreciated!

  • $\begingroup$ did you look into bootstrapping? $\endgroup$ – kjetil b halvorsen Oct 27 '14 at 10:57
  • $\begingroup$ yes I have; I was hoping to find a way to not to have to throw away data, but it looks like this is indeed the way forward. Thanks! $\endgroup$ – saresa Oct 28 '14 at 4:17

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