🚀 go-pugleaf

In article <141430@lll-winken.LLNL.GOV> macq@miguel.llnl.gov (Don MacQueen) writes:
>Some members of the environmental monitoring division
>here are fond of using the median and the median absolute
>deviation from the median (the MAD) as summary statistics for samples
>that have some left censoring.
>
>Does anyone know of any good properties the MAD has?
>(regardless of whether there is censoring)
>
>For instance, the median minimizes the sum of the absolute
>deviations, so perhaps the median absolute deviation makes
>sense as a measure of variability. Is there more to it than
>that?
>
>Thanks
>-- 
>---------------------------------------------------
>Don MacQueen
>preferred                   macq@llnl.gov
>o.k.                        macq@alle.llnl.gov
>Lawrence Livermore Nat. Lab.
>7000 East Ave., L-307          (510) 423-1062
>Livermore, CA 94550
>---------------------------------------------------

The important thing is that the MAD is robust, and hence a more consistent
estimate of error between samples when the samples may contain outliers.

For data that has a gaussian distribution (in which case the mean and
standard deviation are appropriate) the MAD can be related to the
standard error by:
	Stan.Dev. = 1.48 x MAD
This scaling factor can be used to convert the MAD into a number that can
be compared and used as if it were a standard deviation.