MATLAB: Scaled MAD in isoutlier

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I have been using scaled MAD in isoutlier and it has done a wonderful job. However, I wonder what's the mathematical basis of this scaled factor? MAD is a widely used term but I couldn't find any documentation on this -1/(sqrt(2)*erfcinv(3/2)) factor. Some references/literatures would be nice.

Best Answer

Hi,
The c value here is approximately equal to 1.4826 and it is commonly used in outlier detection. It is even mentioned in the MAD wikipedia article: https://en.wikipedia.org/wiki/Median_absolute_deviation
This value assumes that the data is normally distributed. For an example reference, see https://dipot.ulb.ac.be/dspace/bitstream/2013/139499/1/Leys_MAD_final-libre.pdf
Our documentation mentions the c value, but doesn't explicitly state the widely-used approximate value 1.4826 since we actually do the calculation in our isoutlier function.
Hope this helps!.
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