# NAME

Text::NSP::Measures::2D::Fisher2 - Perl module that provides methods to compute the Fishers exact tests.

# SYNOPSIS

### Basic Usage

``````  use Text::NSP::Measures::2D::Fisher2::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;
}``````

# DESCRIPTION

This module provides a framework for the naive implementation of the fishers exact tests. That is the implementation does not have any optimizations for performance. This will compute the factorials for the hypergeometric probabilities using direct multiplications.

This measure should be used if you need exact values without any rounding errors, and you are not worried about the performance of the measure, otherwise use the implementations under the Text::NSP::Measures::2D::Fisher module.

To use this implementation, you will have to specify the entire module name. Usage:

statistic.pl Text::NSP::Measures::Fisher2::left dest.txt source.cnt

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.

A right 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 greater than or equal to the given value. A right sided Fisher's Exact Test tells us how likely it is to randomly sample a table where n11 is greater than observed. In other words, it tells us how likely it is to sample an observation where the two words are more dependent than currently observed.

A twotailed fishers test is calculated by adding the probabilities of all the contingency tables with probabilities less than the probability of the observed table. The twotailed fishers test tells us how likely it would be to observe an contingency table which is less probable than the current table.

## Methods

getValues() -This method calls the computeObservedValues() and the computeExpectedValues() methods to compute the observed and marginal total values. It checks thes values for any errors that might cause the Fishers Exact test measures to fail.

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

RETURN VALUES : 1/undef ..returns '1' to indicate success and an undefined(NULL) value to indicate faliure.

computeDistribution() - This method calculates the probabilities for all the possible tables

INPUT PARAMS : \$n11_start .. the value for the cell 1,1 in the first contingency table \$final_limit .. the value of cell 1,1 in the last contingency table for which we have to compute the probability.

RETURN VALUES : \$probability .. Reference to a hash containg hypergeometric probabilities for all the possible contingency tables

# AUTHOR

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>

# HISTORY

Last updated: \$Id: Fisher2.pm,v 1.10 2006/06/21 11:10:52 saiyam_kohli Exp \$

# BUGS

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

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 http://www.gnu.org/licenses/gpl.txt and is included in this distribution as GPL.txt.