Measuring relative variability for variables with different scales

I want to compare the relative variability of several sleep-related variables in the same group of subjects. For example, is there more variability in time spent in REM sleep compared to the number of eye movement in REM sleep? These variables have different scales, which does not allow me to simply compare their variances.

I have computed several relative measures of variation such as the coefficient of variation (SD/M), coefficient of dispersion (Mean Absolute Deviation from Median/Median) as well as the coefficient of quartile variation (Q3-Q1/Q3+Q1). To provide some context, several of my variables are highly skewed.

My major question is: Is one of these coefficients more appropriate than the others? I know that with skewed data I will probably want to avoid the traditional coefficient of variation. But what about dividing the 'mean absolute deviation from the median' by the median? Would it be better (e.g., more robust) to use the 'median absolute deviation from the median' instead (and divide this value by the median)? I have not seen much discussion of the coefficient of quartile variation. There is also the question of using of the two estimators proposed by Rousseeuw and Croux (1993)- Sn and Qn - could they be used here? These last two measures are not necessarily symmetrical around any measure of location, so I am not sure whether it would be appropriate to use them in this context.

If anyone has any other helpful suggestions, that would be helpful as well.

• Sorry, one more thing - there is always the issue of whether to put confidence intervals around the coefficients described above, and how one might do that. Kevin Apr 24 '13 at 23:12
• It really depends on what you mean by "variability". Toy example: Which set has more variability: (1,2,3,4,5) (1,1,1,1,5), (1,5,1,5,1) etc. Apr 24 '13 at 23:26
• Thanks for your comment Peter. Basically in my area people compare different groups (e.g., young versus older) on these types of sleep measures, but they do so only for measures of location, typically the mean. Also, people sometimes will examine changes in these variables over time, but again, this typically involves the mean. I am interested in how these variables differ from one another in their variability, dispersion, or spread - not just their location. For example, in my older group which variables have the most variability, dispersion, or spread and which ones do not. Apr 25 '13 at 0:14