I have a continuous variable (say, sales volume) that I measure for multiple firms over a time period of ten years (but I do not have data across the full ten years for all firms, some drop out, some enter my sample). I want to show that, for each of these firms, there is not a lot of variation in this continuous variable over time, within any given firm.

Added complication: The continuous variable is logged, so it does not have an intuitive interpretation.

What is the best way to show that there is "not much variation," ideally in a single number?

(And yes, I know that there is no technically "correct" answer to this, and "not much variation" is utterly unspecific; I am really just looking for ways to give a reader a quick intuitive sense of whether there is a lot it not a lot of variation over time)

  • $\begingroup$ What about variance? $\endgroup$ – Tim Nov 9 '16 at 15:43
  • $\begingroup$ Do you suspect that there is also no trend at all and that all the values are close across time? If so a standard measure like variance as @Tim suggests seems fine. $\endgroup$ – dsaxton Nov 9 '16 at 15:58
  • $\begingroup$ so what I would do is calculate the average of all the variances per firm? somehow I had not thought it might be so easy $\endgroup$ – user1769925 Nov 9 '16 at 16:23
  • $\begingroup$ I guess one thing I was confused about is that, of course, each firm will have its own distinct mean. $\endgroup$ – user1769925 Nov 10 '16 at 7:10

If the variability is "small", the standard deviation of the logs will be a reasonable measure of the typical "percentage deviation" from the geometric mean.

e.g. if the standard deviation of the logs is 0.05, that means that a "typical" amount of deviation from the geometric mean is around 5% above or below. (As this gets to much over 0.10 it starts to be less useful as a direct approximation but it's still a good bit smaller than the distinction between root-mean-square deviation and average absolute deviation of the logs, which we're sort of glossing over; if you're happy with that level of glossing over, it's still reasonable up to about 0.25 or even a bit higher).

This standard-deviation-of-the-logs will also be a good approximation to the coefficient of variation when it's small.

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