DIFFERENCE OF MAD

DIFFERENCE OF MAD (LET)

Let Subcommand

Compute the difference between the median absolute deviations (MAD) for two response variables.

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

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

The scaled MAD is defined as

MADN = MAD/0.6745

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

For the differeence of median absolute deviations, the median absolute deviation is computed for each of two samples then their difference is taken.

LET <par> = DIFFERENCE OF MAD <y1> <y2>
                        <SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
            <y2> is the first response variable;
            <par> is a parameter where the computed difference of the median absolute deviations is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET <par> = DIFFERENCE OF SCALED MAD <y1> <y2>
                        <SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
            <y2> is the first response variable;
            <par> is a parameter where the computed difference of the scaled median absolute deviations is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET A = DIFFERENCE OF MAD Y1 Y2
LET A = DIFFERENCE OF MAD Y1 Y2 SUBSET X > 1
LET A = DIFFERENCE OF SCALED MAD Y1 Y2

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

None

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

MAD	= Compute the median absolute deviation.
AAD	= Compute the average absolute deviation.
STANDARD DEVIATION	= Compute the standard deviation.
DIFFERENCE OF AAD	= Compute the difference of average absolute deviations.
DIFFERENCE OF SD	= Compute the difference of standard deviations.
DIFFERENCE OF BIWEIGHT SCALE	= Compute the difference of biweight scales.
DIFFERENCE OF BIWEIGHT MIDVARIANCE	= Compute the difference of biweight midvariances.
STATISTICS PLOT	= Generate a statistic versus subset plot.
BOOTSTRAP PLOT	= Generate a bootstrap plot.
TABULATE	= Perform a tabulation for a specified statistic.

Robust Estimation of Scale

2003/03
2016/02: Added DIFFERENCE OF SCALED MAD

SKIP 25 
READ IRIS.DAT Y1 TO Y4 X 
. 
LET A = DIFFERENCE OF MAD Y1 Y2 
TABULATE DIFFERENCE OF MAD Y1 Y2 X 
. 
XTIC OFFSET 0.2 0.2 
X1LABEL GROUP ID 
Y1LABEL DIFFERENCE OF MAD 
CHAR X 
LINE BLANK 
DIFFERENCE OF MAD PLOT Y1 Y2 X 
CHAR X ALL 
LINE BLANK ALL 
BOOTSTRAP DIFFERENCE OF MAD PLOT Y1 Y2 X  
    

Dataplot generated the following output.

       ***************************************
       **  LET A = DIFFERENCE OF MAD Y1 Y2  **
       ***************************************
  
  
 THE COMPUTED VALUE OF THE CONSTANT A             =  0.39999986E+00
  
  
       ******************************************
       **  TABULATE DIFFERENCE OF MAD Y1 Y2 X  **
       ******************************************
  
  
                 *    Y1       AND Y2
     X           *    DIFFERENCE OF MEDIAN ABSOLUTE
 **********************************************
     1.00000     *   -0.500002E-01
     2.00000     *    0.150000
     3.00000     *    0.200000
  
       GROUP-ID AND STATISTIC WRITTEN TO FILE DPST1F.DAT