Text::NSP::Measures::2D::CHI::phi - Perl module that implements Phi coefficient measure for bigrams.


Basic Usage

  use Text::NSP::Measures::2D::CHI::phi;

  my $npp = 60; my $n1p = 20; my $np1 = 20;  my $n11 = 10;

  $phi_value = calculateStatistic( n11=>$n11,

  if( ($errorCode = getErrorCode()))
    print STDERR $errorCode." - ".getErrorMessage()."\n"";
    print getStatisticName."value for bigram is ".$phi_value."\n"";


This function computes the the square of the traditional formulation of the Phi Coefficient.

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.

 PHI^2 = ((n11 * n22) - (n21 * n21))^2/(n1p * np1 * np2 * n2p)

Note that the value of PHI^2 is equivalent to Pearson's Chi-Squared test multiplied by the sample size, that is:

 Chi-Squared = npp * PHI^2

We use PHI^2 rather than PHI since PHI^2 was employed for collocation identification in:

Church, K. (1991) Concordances for Parallel Text, Seventh Annual Conference of the UW Centre for the New OED and Text Research, Oxford, England.

calculateStatistic() - method to calculate the Phi Coefficient

INPUT PARAMS : $count_values .. Reference of an hash containing the count values computed by the program.

RETURN VALUES : $phi .. phi value for this bigram.

getStatisticName() - Returns the name of this statistic


RETURN VALUES : $name .. Name of the measure.


Ted Pedersen, University of Minnesota Duluth <>

Satanjeev Banerjee, Carnegie Mellon University <>

Amruta Purandare, University of Pittsburgh <>

Bridget Thomson-McInnes, University of Minnesota Twin Cities <>

Saiyam Kohli, University of Minnesota Duluth <>


Last updated: $Id:,v 1.12 2006/06/21 11:10:52 saiyam_kohli Exp $



          author = {Gale, W. and Church, K.},
          title = {A Program for Aligning Sentences in Bilingual Corpora},
          booktitle = {Proceedings of the 29th Annual Meeting of the
                      Association for Computational Linguistics},
          address = {Berkeley, CA},
          year = {1991}
          url = L<>}


Copyright (C) 2000-2006, Ted Pedersen, Satanjeev Banerjee, Amruta Purandare, Bridget Thomson-McInnes and Saiyam Kohli

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

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    The Free Software Foundation, Inc.,
    59 Temple Place - Suite 330,
    Boston, MA  02111-1307, USA.

Note: a copy of the GNU General Public License is available on the web at and is included in this distribution as GPL.txt.