Standard error of the median

Is the following formula right if I want to measure the standard error of the median in case of a small sample with non normal distribution (I’m using python)?

 sigma=np.std(data)
 n=len(data)
 sigma_median=1.253*sigma/np.sqrt(n)

Answer

Based on some of @mary’s comments I think the following is appropriate. She seems to be selecting the median because the sample is small.

If you were selecting median because it’s a small sample that’s not a good justification. You select median because the median is an important value. It says something different from the mean. You might also select it for some statistical calculations because it’s robust against certain problems like outliers or skew. However, small sample size isn’t one of those problems it’s robust against. For example, when sample size gets smaller it’s actually much more sensitive to skew than the mean.

Attribution
Source : Link , Question Author : mary , Answer Author : John

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