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Dataplot Vol 2 Vol 1

COEFFICIENT OF DISPERSION

Name:
    COEFFICIENT OF DISPERSION (LET)
Type:
    Let Subcommand
Purpose:
    Compute the coefficient of dispersion of a variable.
Description:
    The coefficient of dispersion is defined as

      \( \mbox{COD} = \frac{\tau}{\eta} \)

    where \( \eta \) and \( \tau \) are the median and median absolute deviation, respectively.

    This statistic has been suggested as a robust alternative to the coefficient of variation.

Syntax 1:
    LET <par> = COEFFICIENT OF DISPERSION <y>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y> is a response variable;
                <par> is a parameter where the coefficient of dispersion value is saved;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 2:
    LET <par> = DIFFERENCE OF COEFFICIENT OF DISPERSION <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 difference of the coefficient of dispersion values is saved;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET COD = COEFFICIENT OF DISPERSION Y1
    LET COD = COEFFICIENT OF DISPERSION Y1 SUBSET TAG > 2

    LET DIFFCOD = DIFFERENCE OF COEFFICIENT OF DISPERSION Y1 Y2

Note:
    Note that there are various other definitions for the coefficient of dispersion.

    It is sometimes defined as

      COD = VARIANCE/MEAN

    To compute this statistic in Dataplot, use the command

      LET A = INDEX OF DISPERSION Y

    Another definition is

      COD = AAD/MEDIAN

    where AAD is the average absolute deviation. In this case, we are computing the AAD as

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

    where \( \tilde{X} \) denotes the median.

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

    This statistic can be computed in Dataplot using the command

      LET A = AAD TO MEDIAN Y

    Basically, you can define a dispersion index based on a scale statistic (standard deviation, average absolute deviation, median absolute deviation, etc.) divided by a location statistic (mean, median, etc.). So there are additional possibilities not discussed here.

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

Default:
    None
Synonyms:
    None
Related Commands: Reference:
    Bonett and Seier (2005), "Confidence interval for a coefficient of dispersion in nonnormal distributions", Biometrical Journal, Vol. 48, pp. 144-148.

    Gastwirth (1982), "Statistical properties as a measure of tax assessment uniformity", Journal of Statistical Planning Inference, Vol. 6, pp. 1-12.

Applications:
    Data Analysis
Implementation Date:
    2017/01 2017/06: DIFFERENCE OF COEFFICIENT OF DISPERSION added
Program 1:
    SKIP 25
    READ ZARR13.DAT Y
    LET COD = COEFFICIENT OF DISPERSION Y
        
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
    x1label Group
    title Coefficient of Dispersion 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
    .
    character X
    line blank
    .
    set statistic plot reference line average
    coefficient of dispersion plot y x
    .
    set write decimals 5
    tabulate coefficient of dispersion y x
        
    plot generated by sample program

                Cross Tabulate COEFFICIENT OF DISPERSION
     
    (Response Variables: Y        )
    ---------------------------------------------
           X          |    COEFFICIENT OF
    ---------------------------------------------
            1.00000   |           0.00300
            2.00000   |           0.00250
            3.00000   |           0.00251
            4.00000   |           0.00301
            5.00000   |           0.00402
            6.00000   |           0.00702
            7.00000   |           0.00400
            8.00000   |           0.00200
            9.00000   |           0.00251
           10.00000   |           0.00201
        
Program 3:
        SKIP 25
        READ IRIS.DAT Y1 TO Y4 X
        .
        LET A = DIFFERENCE OF COEFFICIENT OF DISPERSION Y1 Y2
        SET WRITE DECIMALS 4
        TABULATE DIFFERENCE OF COEFFICIENT Y1 Y2 X
        
        
                Cross Tabulate DIFFERENCE OF COEFFICIENT OF DISPERSION
     
    (Response Variables: Y1       Y2      )
    ---------------------------------------------
           X          |   DIFFERENCE OF C
    ---------------------------------------------
             1.0000   |           -0.0335
             2.0000   |           -0.0121
             3.0000   |           -0.0051
        
    . XTIC OFFSET 0.2 0.2 X1LABEL GROUP ID Y1LABEL DIFFERENCE OF COEFFICIENT OF DISPERSION CHAR X LINE BLANK DIFFERENCE OF COEFFICIENT OF DISPERSION PLOT Y1 Y2 X

    plot generated by sample program

    CHAR X ALL LINE BLANK ALL BOOTSTRAP DIFFERENCE OF COEFFICIENT OF DISPERSION 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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