UNIFORM CHISQUARE

UNIFORM CHISQUARE (LET)

Let Subcommand

Given a vector of counts, compute the difference from uniformity based on the chi-square statistic.

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, X_i, 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

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

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.

LET A = UNIFORM CHISQUARE Y1
LET A = UNIFORM CHISQUARE Y1 SUBSET TAG > 2

Dataplot statistics can be used in a number of commands. For details, enter
HELP STATISTICS

None

UNIFORM CHI SQUARE

VARIATIONAL DISTANCE	= Compute the variational distance of a variable containing a set of counts.
RELATIVE DISPERSION INDEX	= Compute the relative dispersion index of a variable containing a set of counts.
GOODNESS OF FIT	= Perform a goodness of fit test.

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.

Spatial Statistics

2014/3

 
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