I have tried to find a solution to my question on Google, but I can’t seem to find much information about error bars and median absolute deviation and I do not know much about statistical error analysis so any help would be greatly appreciated.
I am creating a semi-log plot for my astronomy research that splits the data into 5 equally spaced bins in log base 10 (x-axis) and plots the average value for each bin (y-axis). Thus each bin has a larger sample size as the x-axis increases. Since it’s a statistical study there is a lot of potential for uncertainty and there is a high presence of outliers (non-Gaussian error distributions). As a result, I would like to use median absolute deviation (MAD) error bars since MAD is less susceptible to outliers.
So my question is: Much like standard deviation and standard error, where standard error is just stdev/sqrt(N) and N is the size of the sample – is there an analog to this for median absolute deviation? The error bars I get when I use MAD/sqrt(N) look correct, but I am not confident in explaining my reasoning for using this approach. Is dividing MAD by the square root of the sample size an acceptable means to produce error bars? And if not, do you have any other suggestions? Also, from research I’ve done it seems that median absolute deviation is a better estimator than mean absolute deviation…would you agree with this?
Here is my original plot with error bars from median absolute deviation/sqrt(N) (NOTE: title should read median, not mean!) The first bin contains 39 samples, second contains 146, third 454, fourth 1287, and fifth 2371 samples. It looks nice, but the method for producing error bars does not seem very accurate.
I've created error bars using the bootstrap method as suggested by @Glen_b (attached below). It looks good to me, but my advisor feels that the error bars have been overestimated in this method.