# Measures of variability that do not depend on the sample size

I want to compare the range of scores across two samples with differing sample sizes. The usual measures, standard deviation (SE), standard error (SE), and variance all depend on sample size, with n in the denominator of the equation. Despite less reliable estimates of variability for the smaller sample, the inter-quartile range avoids this problem, is that correct? Range (from minimum and maximum) would also be smaller for the smaller sample due to random sampling. Are there other measures of variability that might be applicable in this case? The sample distributions are positively skewed.

• I'm not sure I follow -- $n$ appears in the denominator of variance because it's a kind of average (mean square deviation from the mean) -- why exactly is that a problem? Is a sample quartile really defined without any reference to the sample size? Jul 27, 2021 at 1:54
• Thanks for your reply! If one were to simulate a distribution with a small or large number of observations, the smaller sample would show the smaller variance, or am I misunderstanding? Quartiles don't seem to depend on n in the same way since the estimate is always proportional to the number of observations. Jul 27, 2021 at 2:05
• No, on average two samples of difference size should give about the same variance* ; the numerator of variance has a sum of terms -- more terms for a larger sample. The larger numerator is compensated by a larger denominator. $\:\:$ ... *(they differ slightly in expectation if you don't use the Bessel correction) Jul 27, 2021 at 2:23
• In any case your suggestion of simulation is a good one -- so why not actually do that and see? Jul 27, 2021 at 6:01