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Dataplot Vol 2 Vol 1

DIFFERENCE OF AVERAGE ABSOLUTE DEVIATION FROM MEDIAN

Name:
    DIFFERENCE OF AVERAGE ABSOLUTE DEVIATION FROM MEDIAN (LET)
Type:
    Let Subcommand
Purpose:
    Compute the difference between the average absolute deviations from the median for two response variables.
Description:
    The average absolute deviation from the median is defined as

    \[ \mbox{AAD} = \frac{\sum_{i=1}^{N}{|X - \tilde{X}|}}{N} \]

    where \( \tilde{X} \) is the median of the variable, and N is the number of observations. This statistic is sometimes used as an alternative to the standard deviation.

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

Syntax:
    LET <par> = DIFFERENCE OF AVERAGE ABSOLUTE DEVIATION FROM MEDIAN <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 average absolute deviations from the median is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = DIFFERENCE OF AVERAGE ABSOLUTE DEVIATION FROM MEDIAN Y1 Y2
Note:
    Prior to the 2014/07 version, the AVERAGE ABSOLUTE DEVIATION command computed the difference from the median rather than the mean. The 2014/07 version corrected this command to compute differences from the mean and added the commands

      AVERAGE ABSOLUTE DEVIATION FROM THE MEDIAN
      DIFFERENCE OF AVERAGE ABSOLUTE DEVIATION FROM MEDIAN

    to compute differences from the median.

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

Default:
    None
Synonyms:
    None
Related Commands: Applications:
    Data Analysis
Implementation Date:
    2014/07: Original implementation
Program:
     
    SKIP 25
    READ IRIS.DAT Y1 TO Y4 X
    .
    LET A = DIFFERENCE OF AAD Y1 Y2
    SET WRITE DECIMALS 4
    TABULATE DIFFERENCE OF AAD Y1 Y2 X
        
    The following output is generated
     
                Cross Tabulate DIFFERENCE OF AVERAGE ABSOLUTE DEVIATION
     
    (Response Variables: Y1       Y2      )
    ---------------------------------------------
           X          |   DIFFERENCE OF A
    ---------------------------------------------
      0.1000000E+01   |    -0.1664000E-01
      0.2000000E+01   |     0.1666400E+00
      0.3000000E+01   |     0.2604000E+00
        
     
    .
    XTIC OFFSET 0.2 0.2
    X1LABEL GROUP ID
    Y1LABEL DIFFERENCE OF AAD
    CHAR X
    LINE BLANK
    DIFFERENCE OF AAD PLOT Y1 Y2 X
    CHAR X ALL
    LINE BLANK ALL
    BOOTSTRAP DIFFERENCE OF AAD PLOT Y1 Y2 X 
        

    plot generated by sample program

    plot generated by sample program

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Date created: 01/31/2015
Last updated: 11/02/2015

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