Median absolute deviation from median

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2 total messages Started by Don MacQueen Sat, 14 Nov 1992 00:39

#598

Author: Don MacQueen
Date: Sat, 14 Nov 1992 00:39

23 lines
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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
---------------------------------------------------

Re: Median absolute deviation from median

#662

Author: Tom Hearn
Date: Mon, 16 Nov 1992 17:26

34 lines
1841 bytes

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.

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