```
=head1 NAME
Text::NSP::Measures::2D::Fisher::left - Perl module implementation of the left sided
Fisher's exact test.
=head1 SYNOPSIS
=head3 Basic Usage
use Text::NSP::Measures::2D::Fisher::left;
my $npp = 60; my $n1p = 20; my $np1 = 20; my $n11 = 10;
$left_value = calculateStatistic( n11=>$n11,
n1p=>$n1p,
np1=>$np1,
npp=>$npp);
if( ($errorCode = getErrorCode()))
{
print STDERR $errorCode." - ".getErrorMessage();
}
else
{
print getStatisticName."value for bigram is ".$left_value;
}
=head1 DESCRIPTION
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 fishers exact tests are calculated by fixing the marginal totals
and computing the hypergeometric probabilities for all the possible
contingency tables,
A left sided test is calculated by adding the probabilities of all
the possible two by two contingency tables formed by fixing the
marginal totals and changing the value of n11 to less than the given
value. A left sided Fisher's Exact Test tells us how likely it is to
randomly sample a table where n11 is less than observed. In other words,
it tells us how likely it is to sample an observation where the two words
are less dependent than currently observed.
=head2 Methods
=over
=cut
package Text::NSP::Measures::2D::Fisher::left;
use Text::NSP::Measures::2D::Fisher;
use strict;
use Carp;
use warnings;
no warnings 'redefine';
require Exporter;
our ($VERSION, @EXPORT, @ISA);
@ISA = qw(Exporter);
@EXPORT = qw(initializeStatistic calculateStatistic
getErrorCode getErrorMessage getStatisticName);
$VERSION = '0.97';
=item calculateStatistic() - This method computes the left sided Fishers
exact test.
INPUT PARAMS : $count_values .. Reference of an array containing
the count values computed by the
count.pl program.
RETURN VALUES : $left .. Left Fisher value.
=cut
sub calculateStatistic
{
my %values = @_;
my $probabilities;
# computes and returns the observed and marginal values from
# the frequency combination values. returns 0 if there is an
# error in the computation or the values are inconsistent.
if( !(Text::NSP::Measures::2D::Fisher::getValues(\%values)) )
{
return;
}
my $final_limit = $n11;
my $n11_start = $n1p + $np1 - $npp;
if($n11_start<0)
{
$n11_start = 0;
}
if( !($probabilities = Text::NSP::Measures::2D::Fisher::computeDistribution($n11_start, $final_limit)))
{
return;
}
my $key_n11;
my $leftfisher=0;
foreach $key_n11 (sort { $a <=> $b } keys %$probabilities)
{
if($key_n11>$final_limit)
{
last;
}
$leftfisher += exp($probabilities->{$key_n11});
}
return $leftfisher;
}
=item getStatisticName()
Returns the name of this statistic
INPUT PARAMS : none
RETURN VALUES : $name .. Name of the measure.
=cut
sub getStatisticName
{
return "Left Fisher";
}
1;
__END__
=back
=head1 AUTHOR
Ted Pedersen, University of Minnesota Duluth
E<lt>tpederse@d.umn.eduE<gt>
Satanjeev Banerjee, Carnegie Mellon University
E<lt>satanjeev@cmu.eduE<gt>
Amruta Purandare, University of Pittsburgh
E<lt>amruta@cs.pitt.eduE<gt>
Bridget Thomson-McInnes, University of Minnesota Twin Cities
E<lt>bthompson@d.umn.eduE<gt>
Saiyam Kohli, University of Minnesota Duluth
E<lt>kohli003@d.umn.eduE<gt>
=head1 HISTORY
Last updated: $Id: left.pm,v 1.12 2006/06/21 11:10:52 saiyam_kohli Exp $
=head1 BUGS
=head1 SEE ALSO
@inproceedings{Pedersen96,
author = {Pedersen, T.},
title = {Fishing For Exactness},
booktitle = {Proceedings of the South Central SAS User's
Group (SCSUG-96) Conference},
year = {1996},
pages = {188--200},
month ={October},
address = {Austin, TX}
url = L<http://www.d.umn.edu/~tpederse/pubs.html>}
L<http://groups.yahoo.com/group/ngram/>
L<http://www.d.umn.edu/~tpederse/nsp.html>
=head1 COPYRIGHT
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.
You should have received a copy of the GNU General Public License along
with this program; if not, write to
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 L<http://www.gnu.org/licenses/gpl.txt> and is included in this
distribution as GPL.txt.
=cut
```