Statistics::Gtest version 0.07 ============================== 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 Carp 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.