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# Manual Reference Pages  -  TEXT::NSP::MEASURES::2D::CHI (3)

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### NAME

Text::NSP::Measures::2D::CHI - Perl module that provides error checks
for the Pearson’s chi squared, phi coefficient
and the Tscore measures.

### SYNOPSIS

Basic Usage

```

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"";
}

```

### DESCRIPTION

This module is the base class for the Chi-squared and Phi coefficient measures. This module provides error checks specific for these measures, it also implements the computations that are common to these measures.
Pearson’s Chi-Squared
```

x2 = 2 * [((n11 - m11)/m11)^2 + ((n12 - m12)/m12)^2 +
((n21 - m21)/m21)^2 + ((n22 -m22)/m22)^2]

```
Phi Coefficient
```

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

```
T-Score
```

tscore = (n11 - m11)/sqrt(n11)

```
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

Although T-score seems quite different from the other two measures we
have put it in the CHI family because like the other two measures it
uses the difference between the observed and expected values and is also
quite similar in ranking the bigrams.

```
getValues() - This method calls the computeMarginalTotals(), computeObservedValues() and the computeExpectedValues() methods to compute the observed and expected values. It checks thees values for any errors that might cause the PHI and x2 measures to fail. INPUT PARAMS : \$count_values .. Reference of an hash 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
failure.

computeVal() - Computes the deviation in observed value with respect to the expected values INPUT PARAMS : \$n ..Observed value
\$m ..Expected value

RETURN VALUES : (n-m)^2/m ..the log of the ratio of
observed value to expected
value.

### 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: CHI.pm,v 1.14 2008/03/26 17:18:26 tpederse Exp \$

### SEE ALSO

<http://groups.yahoo.com/group/ngram/>

<http://www.d.umn.edu/~tpederse/nsp.html>

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

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