Is there any universal criterion that permits to say that there is small or large variability? For example, I plan to conduct an experiment. I would like to say that if obtain small variability, I will do X, but if it is large then I will do Y. But how I define what is “small” and what is “large”? Standard deviation depends on the sample size, so probably my question does not make sense.

  • $\begingroup$ Standard deviation does not depend on sample size. The adequate metric totally depends on your data and where you want to draw the line, there won't be any universal way. $\endgroup$ – Romain Reboulleau Oct 7 '18 at 12:11
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    $\begingroup$ Suppose there were a definitive answer. For instance, imagine (hypothetically) that any SD between 0 and 1 is considered "small," between 1 and 3 is "medium," and greater than 3 is "large." Now suppose your experiment measures the time to drive between two nearby cities. If you report the time in hours, the SD of your results is 0.25, which is "small," but if you report the time in minutes it is 15, which is "large." Note, too, that (1) the SD does not depend on sample size and (2) your conclusions are perfectly arbitrary because they depend on your arbitrary choice of units of time. $\endgroup$ – whuber Oct 7 '18 at 12:35
  • $\begingroup$ The problem with units I can probably solve if I do some normalization to data prior to calculating std... $\endgroup$ – student Oct 7 '18 at 15:05
  • $\begingroup$ What is the expected distribution of your data? If, for ex., you know that your data is Poisson distributed, you could calculate the mean of your sample and compare it with a theoretical Poisson distribution with that mean, to see how much different (more / less spread out) your sample distribution is. $\endgroup$ – user2974951 Oct 8 '18 at 6:38

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