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For an experiment I'm analyzing, I took many measurements of many different values. (To make it concrete, let's pretend I measured the height of people from many different age groups -- I have the height of ten 20-year-olds, ten 21-year-olds, ten 22-year-olds, etc.)

I'd like to demonstrate that the variance of all my readings, per variable, is pretty low. (In my example, I'd like to show that people of any given age are all about the same height. That is, say 20-year-olds are all close to 5'4" with low variance and 21-year-olds are all close to 5'6". The particular heights don't matter; just that people of any given age are similar in height to other people of that age. That's obviously not true, but let's pretend it is.)

What's the best metric to report? I could, for example, take the arithmetic mean of the variances -- or maybe the harmonic mean or geometric mean would be better? Or perhaps I should be averaging the standard deviations or the standard errors?

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  • $\begingroup$ I think that your pretend example doesn't match your real case. In the pretend example, if you want to show that people of a given age are about the same height, you can just report the variance of height for that age. But if you'd like to show that ALL the people of a given age are about the same height, I'd report the range of values. But then you start talking about measures that combine the variances or something across different groups. So apparently you want to say something not about people of a particular age, but about people of different ages. But what do you want to show? $\endgroup$
    – Peter Flom
    Commented Sep 9, 2011 at 20:48
  • $\begingroup$ Yes; I should have made this clearer. I'll try to clarify the wording above. I'm interested in showing that people of ANY given age are, regardless of the particular age, around the same height. $\endgroup$
    – adrian
    Commented Sep 9, 2011 at 20:56

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What you want to show does not boil down to any statistical test. It's a descriptive matter. Merely by reporting the mean and standard deviation within each group, you'll be demonstrating the extent to which people within each group are "around the same height." You'll probably find that showing a series of histograms (especially if paneled as part of a single display) or boxplots (especially if grouped into one display) will make your point even more effectively.

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  • $\begingroup$ You're probably right -- I've made a few combined box plots and it seems to get the point across better than an aggregate number would. Thanks! $\endgroup$
    – adrian
    Commented Sep 11, 2011 at 4:02

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