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Dataplot Vol 2 Vol 1

UNIFORM CHISQUARE

Name:
    UNIFORM CHISQUARE (LET)
Type:
    Let Subcommand
Purpose:
    Given a vector of counts, compute the difference from uniformity based on the chi-square statistic.
Description:
    In spatial analysis, it is sometimes desired to determine if the points in the given space are consistent with a uniform distribution. Given a set of N counts, Xi, one such measure is based on the chi-square statistic which is defined as

      \( \chi^{2} = \sum_{i=1}^{k}{\frac{(X_{i} - \mbox{EXP})^2} {\mbox{EXP}}} \)

    where

      \( \mbox{EXP} = \frac{\sum_{i=1}^{k}{X_{i}}} {k} \)
Syntax:
    LET <a> = UNIFORM CHISQUARE <y>
                      <SUBSET/EXCEPT/FOR qualification>
    where <y> is the response variable;
                <a> is a parameter where the computed statistic is saved;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = UNIFORM CHISQUARE Y1
    LET A = UNIFORM CHISQUARE Y1 SUBSET TAG > 2
Note:
    Dataplot statistics can be used in a number of commands. For details, enter

Default:
    None
Synonyms:
    UNIFORM CHI SQUARE
Related Commands: Reference:
    Kashiwagi, Fagan, Douglas, Yamamoto, Heckert, Leigh, Obrzut, Du, Lin-Gibson, Mu, Winey, Haggennueller (2007), "Relationship between dispersion metric and properties of PMMA/SWNT nanocomposites", Polymer Journal, Vol. 48, pp. 4855 - 4866.
Applications:
    Spatial Statistics
Implementation Date:
    2014/3
Program:
     
    LET Y  = UNIFORM RANDOM NUMBERS FOR I = 1 1 1000
    LET Y1 X1 = BINNED Y
    LET Y  = NORMAL RANDOM NUMBERS FOR I = 1 1 1000
    LET Y2 X2 = BINNED Y
    LET Y  = EXPONENTIAL RANDOM NUMBERS FOR I = 1 1 1000
    LET Y3 X3 = BINNED Y
    LET A1 = UNIFORM CHISQUARE Y1
    LET A2 = UNIFORM CHISQUARE Y2
    LET A3 = UNIFORM CHISQUARE Y3
    SET WRITE DECIMALS 4
    PRINT A1 A2 A3
        
    The following output is generated.
     PARAMETERS AND CONSTANTS--
    
        A1      --        32.1920
        A2      --       793.6520
        A3      --      1691.2492
        

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Date created: 06/23/2014
Last updated: 06/23/2014

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