SED navigation bar go to SED home page go to Dataplot home page go to NIST home page SED Home Page SED Staff SED Projects SED Products and Publications Search SED Pages
Dataplot Vol 2 Vol 1

INDEX OF DISPERSION

Name:
    INDEX OF DISPERSION (LET)
Type:
    Let Subcommand
Purpose:
    Compute the index of dispersion of a variable.
Description:
    The sample index of dispersion is defined as the ratio of the variance to the mean:

      \( \mbox{d} = \frac{s^2}{\bar{x}} \)

    where s2 is the sample variance and \( \bar{x} \) is the sample mean. That is, it shows the variability, as defined by the variance, relative to the mean.

    The index of dispersion is related to the coefficient of variation (the ratio of the standard deviation to the mean) and the coefficient of dispersion (the ratio of the median absolute deviation to the median). The index of dispersion is also referred to the coefficient of dispersion. However, Dataplot reserves this term for the ratio of the median absolute deviation to the mean.

    The index of dispersion should typically only be used for data measured on a ratio scale. That is, the data should be have a meaningful zero. The index of dispersion is sometimes used for count data. If the count data follows a Poisson distribution, then the mean and variance should be equal and the index of dispersion is 1. If the counts follow a geometric or negative binomial, then the index of dispersion should be greater than 1. If the counts follow a binomial distribution, the index of dispersion should be less than 1.

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

    LET D = DIFFERENCE OF INDEX OF DISPERSION Y1 Y2

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
    2017/06: Added DIFFERENCE OF INDEX OF DISPERSION
Program 1:
     
    LET LAMBDA = 2.9
    LET Y1 = POISSON RANDOM NUMBERS FOR I = 1 1 100
    LET D = INDEX OF DISPERSION 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 Index of Dispersion
    x1label Group
    title Index 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
    y1tic mark label decimals 3
    .
    character X
    line blank
    .
    set statistic plot reference line average
    index of dispersion plot y x
    .
    tabulate index of dispersion y x
        
    plot generated by sample program
                Cross Tabulate INDEX OF DISPERSION
     
    (Response Variables: Y        )
    ---------------------------------------------
           X          |   INDEX OF DISPER
    ---------------------------------------------
           1.000000   |          0.000019
           2.000000   |          0.000027
           3.000000   |          0.000016
           4.000000   |          0.000015
           5.000000   |          0.000058
           6.000000   |          0.000098
           7.000000   |          0.000062
           8.000000   |          0.000013
           9.000000   |          0.000017
          10.000000   |          0.000029
        
Program 3:
     
    SKIP 25
    READ IRIS.DAT Y1 TO Y4 X
    .
    LET A = DIFFERENCE OF INDEX OF DISPERSION Y1 Y2
    SET WRITE DECIMALS 4
    TABULATE DIFFERENCE OF INDEX OF DISPERSION Y1 Y2 X
    
    
                Cross Tabulate DIFFERENCE OF INDEX OF DISPERSION
     
    (Response Variables: Y1       Y2      )
    ---------------------------------------------
           X          |   DIFFERENCE OF I
    ---------------------------------------------
             1.0000   |           -0.0171
             2.0000   |            0.0093
             3.0000   |            0.0264
    
    . XTIC OFFSET 0.2 0.2 X1LABEL GROUP ID Y1LABEL DIFFERENCE OF INDEX OF DISPERSION CHAR X LINE BLANK DIFFERENCE OF INDEX OF DISPERSION PLOT Y1 Y2 X

    plot generated by sample program

    CHAR X ALL LINE BLANK ALL BOOTSTRAP DIFFERENCE OF INDEX OF DISPERSION PLOT Y1 Y2 X

    plot generated by sample program

Privacy Policy/Security Notice
Disclaimer | FOIA

NIST is an agency of the U.S. Commerce Department.

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

Please email comments on this WWW page to alan.heckert.gov.