MEDIAN ABSOLUTE DEVIATION

MEDIAN ABSOLUTE DEVIATION (LET)

Let Subcommand

Compute the median absolute deviation for a variable.

The median absolute deviation is:
\( \mbox{MAD} = \mbox{median} |x - \tilde{x}| \)

where \( \tilde{x} \) is the median of the variable. This statistic is sometimes used as a robust alternative to the standard deviation as a measure of scale.

The scaled MAD is defined as

MADN = MAD/0.6745

For normally distributed data, the scaled MAD is approximately equal to the standard deviation.

LET <par> = MEDIAN ABSOLUTE DEVIATION <y>
                        <SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
            <par> is a parameter where the computed median absolute deviation is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET <par> = SCALED MEDIAN ABSOLUTE DEVIATION <y>
                        <SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
            <par> is a parameter where the computed scaled median absolute deviation is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET A = MEDIAN ABSOLUTE DEVIATION Y1
LET A = MEDIAN ABSOLUTE DEVIATION Y1 SUBSET TAG > 2
LET A = SCALED MEDIAN ABSOLUTE DEVIATION Y1

Dataplot statistics can be used in a number of commands. For details, enter
HELP STATISTICS

None

MAD is a synonym for MEDIAN ABSOLUTE DEVIATION
MADN is a synonym for SCALED MEDIAN ABSOLUTE DEVIATION
NORMALIZED is a synomym for SCALED

AVERAGE ABSOLUTE DEVIATION	= Compute the average absolute deviation of a variable.
STANDARD DEVIATION	= Compute the standard deviation of a variable.
VARIANCE	= Compute the variance of a variable.
RANGE	= Compute the range of a variable.

Robust Statistics

1995/04
2016/02: Added SCALED MEDIAN ABSOLUTE DEVIATION

 
LET Y1 = LOGISTIC RANDOM NUMBERS FOR I = 1 1 100
LET A1 = MEDIAN ABSOLUTE DEVIATION Y1
LET A2 = SCALED MEDIAN ABSOLUTE DEVIATION Y1
    

 
SKIP 25
READ GEAR.DAT DIAMETER BATCH
TITLE AUTOMATIC
XLIMITS 1 10
MAJOR XTIC MARK NUMBER 10
MINOR XTIC MARK NUMBER 0
XTIC OFFSET 1 1
X1LABEL BATCH
Y1LABEL MEDIAN ABSOLUTE DEVIATION OF DIAMETER
MAD PLOT DIAMETER BATCH