Text::NSP::Measures::2D::CHI::x2 - Perl module that implements Pearson's chi squared measure of association for bigrams.
use Text::NSP::Measures::2D::CHI::x2; my $npp = 60; my $n1p = 20; my $np1 = 20; my $n11 = 10; $x2_value = calculateStatistic( n11=>$n11, n1p=>$n1p, np1=>$np1, npp=>$npp); if( ($errorCode = getErrorCode())) { print STDERR $errorCode." - ".getErrorMessage()."\n""; } else { print getStatisticName."value for bigram is ".$x2_value."\n""; }
Pearson's Chi-squred test measures the devitation between the observed data and what would be expected if <word1> and <word2> were independent. The higher the score, the less evidence there is in favor of concluding that the words are independent.
Assume that the frequency count data associated with a bigram <word1><word2> is stored in a 2x2 contingency table:
word2 ~word2 word1 n11 n12 | n1p ~word1 n21 n22 | n2p -------------- np1 np2 npp
where n11 is the number of times <word1><word2> occur together, and n12 is the number of times <word1> occurs with some word other than word2, and n1p is the number of times in total that word1 occurs as the first word in a bigram.
The expected values for the internal cells are calculated by taking the product of their associated marginals and dividing by the sample size, for example:
np1 * n1p m11= --------- npp
Then the deviation between observed and expected values for each internal cell is computed to arrive at the Pearson's Chi-Squared test value:
Pearson's Chi-Squared = 2 * [((n11 - m11)/m11)^2 + ((n12 - m12)/m12)^2 + ((n21 - m21)/m21)^2 + ((n22 -m22)/m22)^2]
INPUT PARAMS : $count_values .. Reference of an hash containing the count values computed by the count.pl program.
RETURN VALUES : $x2 .. x2 value for this bigram.
INPUT PARAMS : none
RETURN VALUES : $name .. Name of the measure.
Ted Pedersen, University of Minnesota Duluth <tpederse@d.umn.edu>
Satanjeev Banerjee, Carnegie Mellon University <satanjeev@cmu.edu>
Amruta Purandare, University of Pittsburgh <amruta@cs.pitt.edu>
Bridget Thomson-McInnes, University of Minnesota Twin Cities <bthompson@d.umn.edu>
Saiyam Kohli, University of Minnesota Duluth <kohli003@d.umn.edu>
Last updated: $Id: x2.pm,v 1.10 2006/06/21 11:10:52 saiyam_kohli Exp $
http://groups.yahoo.com/group/ngram/
http://www.d.umn.edu/~tpederse/nsp.html
Copyright (C) 2000-2006, Ted Pedersen, Satanjeev Banerjee, Amruta Purandare, Bridget Thomson-McInnes and Saiyam Kohli
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