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Dataplot Vol 2 Vol 1

DIFFERENCE OF MAD

Name:
    DIFFERENCE OF MAD (LET)
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

      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.

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
    MADN is a synonym for SCALED MAD
    NORMALIZED is a synonym for SCALED
Related Commands: Applications:
    Robust Estimation of Scale
Implementation Date:
    2003/03
    2016/02: Added DIFFERENCE OF SCALED MAD
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 
    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
        
    plot generated by sample program

    plot generated by sample program

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

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