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I wonder if there is a way to estimate error propagation of the mad (=median absolute deviation) for the difference between two median distributions, similar to how you estimate error propagation for the standard deviation for the difference between two average distributions?

I want to compare the difference between two average size distributions and the difference between two median size distributions for the same data set, and I would like to compare the uncertainties by putting the corresponding form of propagated errors as error bars on each plot.

Is there some way to do this or some other way to represent the errors for the median difference distribution?

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