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Dataplot Vol 2 Vol 1

AAD TO MEDIAN

Name:
    AAD TO MEDIAN (LET)
Type:
    Let Subcommand
Purpose:
    Compute the coefficient of dispersion based on the average absolute deviation (AAD) and the median of a variable.
Description:
    There are a number of definitions for the coefficient of dispersion. Dataplot uses the definition based on the ratio of the median absolute deviation (MAD) to the median. An alternative definition is based on the AAD and the median. Specifically,

      \( \mbox{d} = \frac{\mbox{AAD}}{\tilde{x}} \)

    where AAD and \( \tilde{x} \) denote the average absolute deviation and the median, respectively. This is the statistic computed by this command.

    Note that the AAD used here is defined as

      \( \mbox{AAD} = \frac{\sum_{i=1}^{n}{|X_{i} - \tilde{x}|}} {n} \)

    That is, we compute the deviations from the median rather than the mean.

    This statistic is a robust alternative to the coefficient of variation.

Syntax 1:
    LET <par> = AAD TO MEDIAN <y>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y> is a response variable;
                <par> is a parameter where the AAD TO MEDIAN value is saved;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 2:
    LET <par> = DIFFERENCE OF AAD TO MEDIAN <y1> <y2>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y1> is the first response variable;
                <y2> is the second response variable;
                <par> is a parameter where the AAD TO MEDIAN value is saved;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET D = AAD TO MEDIAN Y1
    LET D = AAD TO MEDIAN Y1 SUBSET TAG > 2

    LET D = DIFFERENCE OF AAD TO MEDIAN Y1

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:
    2017/01
Program 1:
     
    LET Y1 = DOUBLE EXPONENTIAL NUMBERS FOR I = 1 1 100
    LET D = AAD TO MEDIAN Y1
        
Program 2:
     
    . Step 1:   Create the data
    .
    skip 25
    read gear.dat y x
    skip 0
    set write decimals 6
    .
    . Step 2:   Define plot control
    .
    title case asis
    title offset 2
    label case asis
    .
    y1label Coefficient of Dispersion (AAD to Median)
    x1label Group
    title AAD to Median for GEAR.DAT
    let ngroup = unique x
    xlimits 1 ngroup
    major x1tic mark number ngroup
    minor x1tic mark number 0
    tic mark offset units data
    x1tic mark offset 0.5 0.5
    y1tic mark label decimals 3
    .
    character X
    line blank
    .
    set statistic plot reference line average
    aad to median plot y x
    .
    tabulate aad to median y x
        
    plot generated by sample program
                 Cross Tabulate AAD TO MEDIAN
      
     (Response Variables: Y        )
     ---------------------------------------------
            X          |     AAD TO MEDIAN
     ---------------------------------------------
            1.000000   |          0.003405
            2.000000   |          0.003704
            3.000000   |          0.002811
            4.000000   |          0.003210
            5.000000   |          0.006134
            6.000000   |          0.007419
            7.000000   |          0.005497
            8.000000   |          0.002800
            9.000000   |          0.003106
           10.000000   |          0.003815
        
Program 3:
     
    SKIP 25
    READ IRIS.DAT Y1 TO Y4 X
    .
    LET A = DIFFERENCE OF AAD TO MEDIAN Y1 Y2
    SET WRITE DECIMALS 4
    TABULATE DIFFERENCE OF AAD TO MEDIAN Y1 Y2 X
    
    
                 Cross Tabulate DIFFERENCE OF AAD TO MEDIAN
      
     (Response Variables: Y1       Y2      )
     ---------------------------------------------
            X          |   DIFFERENCE OF A
     ---------------------------------------------
              1.0000   |           -0.0295
              2.0000   |           -0.0181
              3.0000   |           -0.0036
    
    . XTIC OFFSET 0.2 0.2 X1LABEL GROUP ID Y1LABEL DIFFERENCE OF AAD TO MEDIAN CHAR X LINE BLANK DIFFERENCE OF AAD TO MEDIAN PLOT Y1 Y2 X

    plot generated by sample program

    CHAR X ALL LINE BLANK ALL BOOTSTRAP DIFFERENCE OF AAD TO MEDIAN PLOT Y1 Y2 X

    plot generated by sample program

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Date created: 01/24/2017
Last updated: 06/30/2017

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