                    Statistics::Gtest version 0.04
                    ==============================

NAME
    Statistics::Gtest - calculate G-statistic for tabular data

SYNOPSIS
       use Statistics::Gtest;

       $gt = Statistics::Gtest->new($data);
    
        $degreesOfFreedom = $gt->getDF();
        $gstat = $gt->getG();
    
        $gt->setExpected($expectedvalues);
        $uncorrectedG = $gt->getRawG();
    
DESCRIPTION
    "Statistics::Gtest" is a class that calculates the G-statistic for
    goodness of fit for frequency data. It can be used on simple frequency
    distributions (1-way tables) or for analyses of independence (2-way
    tables).

    Note that "Statistics::Gtest" will not, by itself, perform the
    significance test for you -- it just provides the G-statistic that can
    then be compared with the chi-square distribution to determine
    significance.

OVERVIEW and EXAMPLES
    A goodness of fit test attempts to determine if an observed frequency
    distribution differs significantly from a hypothesized frequency
    distribution. From "Statistics::Gtest"'s point of view, these tests come
    in two flavors: 1-way tests (where a single frequency distribution is
    tested against an expected distribution) and 2-way tests (where a matrix
    of observed values is tested for independence -- that is, the lack of
    interaction effects among the two axes being measured).

    A simple example might help here. You've grown 160 plants from seed
    produced by a single parent plant. You observe that among the offspring
    plants, some have spiny leaves, some have hairy leaves, and some have
    smooth leaves. What is the likelihood that the distribution of this
    trait follows the expected values for simple Mendelian inheritance?

     Observed values:
       Spiny Hairy Smooth
         95    53    12

     Expected values (for a 9:3:3:1 ratio):
         90    60    10

    If the observed and expected values are put into two files,
    "Statistics::Gtest" can create a G-statistic object that will calculate
    the likelihood that the observed distribution is significantly different
    from the distribution that would be expected by simple inheritance. (The
    value of G for this comparison is approximately 1.495, with 2 degrees of
    freedom; the observed results are not significantly different from
    expected at the .05 -- or even .1 level.)

    2-way tests will usually not need a table of expected values, as the
    expected values are generated from the observed value sums. However, one
    can be loaded for 2-way tables as well.

    To determine if the calculated G statistic indicates a statistically
    significant result, you will need to look up the values in a chi-square
    distribution on your own, or make use of the "Statistics::Distributions"
    module:

     use Statistics::Gtest;
     use Statistics::Distributions;

     ...

     my $gt = Statistics::Gtest->new($data);
     my $df = $gt->getDF();
     my $g = $gt->getG();
     my $sig = '.05';
     my $chis=Statistics::Distributions::chisqrdistr ($df,$sig);
     if ($g > $chis) {
       print "$g: Sig. at the $sv level. ($chis cutoff)\n"
     } 

    By default, "Statistics::Gtest" returns a G statistic that has been
    modified by William's correction (Williams 1976). This correction
    reduces the value of G for smaller sample sizes, and has progressively
    less effect as the sample size increases. The raw, uncorrected G
    statistic is also available.

    Calculation methods based on Sokal, R.R., and F.J. Rohlf, Biometry.
    1981. W.H. Freeman and Company, San Francisco.

    Williams, D.A. 1976. Improved likelihood ratio test for complete
    contingency tables. Biometrika, 63:33 - 37.

INSTALLATION

    To install this module type the following:

    perl Makefile.PL ARGS (see the ExtUtils::MakeMaker documentation for
                           possible arguments)
    make
    make test
    make install

DEPENDENCIES

    IO::File

COPYRIGHT AND LICENCE

    Copyright (C) 2007 by David Fleck

    This library is free software; you can redistribute it and/or modify
    it under the same terms as Perl itself, either Perl version 5.8.4 or,
    at your option, any later version of Perl 5 you may have available.
         
