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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

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

    with \( \eta \) and \( \tau \) denoting the median and mean absolute deviation from the median, 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

    Note that 11/2017 version of Dataplot modified the scale factor to be the average absolute deviation from the median rather than the median absolute deviation from the median. This was done to be consistent with the Bonett paper.

    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
    2017/11: Modified the definition to use the average absolute
                    deviation from the median rather than the median absolute
                    deviation from the median
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   |           0.00341
            2.00000   |           0.00370
            3.00000   |           0.00281
            4.00000   |           0.00321
            5.00000   |           0.00613
            6.00000   |           0.00742
            7.00000   |           0.00550
            8.00000   |           0.00280
            9.00000   |           0.00311
           10.00000   |           0.00382
        
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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