 Dataplot Vol 2 Vol 1

Name:
Type:
Let Subcommand
Purpose:
Compute the difference between the median absolute deviations (MAD) for two response variables.
Description:
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

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.

Syntax 1:
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.
Syntax 2:
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.
Examples:
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
Note:
Dataplot statistics can be used in a number of commands. For details, enter

Default:
None
Synonyms:
MEDIAN ABSOLUTE DEVIATION is a synonym for MAD
NORMALIZED is a synonym for SCALED
Related Commands:
 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.
Applications:
Robust Estimation of Scale
Implementation Date:
2003/03
Program:
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
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 NIST is an agency of the U.S. Commerce Department.

Date created: 03/27/2003
Last updated: 11/09/2015