<!DOCTYPE html>

<html>
  <head>
    <meta charset="utf-8">
    
    <title>scipy.stats.fisher_exact &mdash; SciPy v1.1.0.dev0+4e64658 Reference Guide</title>
    
    <link rel="stylesheet" type="text/css" href="../_static/css/spc-bootstrap.css">
    <link rel="stylesheet" type="text/css" href="../_static/css/spc-extend.css">
    <link rel="stylesheet" href="../_static/scipy.css" type="text/css" >
    <link rel="stylesheet" href="../_static/pygments.css" type="text/css" >
    
    <script type="text/javascript">
      var DOCUMENTATION_OPTIONS = {
        URL_ROOT:    '../',
        VERSION:     '1.1.0.dev0+4e64658',
        COLLAPSE_INDEX: false,
        FILE_SUFFIX: '.html',
        HAS_SOURCE:  false
      };
    </script>
    <script type="text/javascript" src="../_static/jquery.js"></script>
    <script type="text/javascript" src="../_static/underscore.js"></script>
    <script type="text/javascript" src="../_static/doctools.js"></script>
    <script type="text/javascript" src="../_static/scipy-mathjax/MathJax.js?config=scipy-mathjax"></script>
    <script type="text/javascript" src="../_static/js/copybutton.js"></script>
    <link rel="index" title="Index" href="../genindex.html" >
    <link rel="search" title="Search" href="../search.html" >
    <link rel="top" title="SciPy v1.1.0.dev0+4e64658 Reference Guide" href="../index.html" >
    <link rel="up" title="Statistical functions (scipy.stats)" href="../stats.html" >
    <link rel="next" title="scipy.stats.ppcc_max" href="scipy.stats.ppcc_max.html" >
    <link rel="prev" title="scipy.stats.contingency.margins" href="scipy.stats.contingency.margins.html" > 
  </head>
  <body>

  <div class="container">
    <div class="header">
    </div>
  </div>


    <div class="container">
      <div class="main">
        
	<div class="row-fluid">
	  <div class="span12">
	    <div class="spc-navbar">
              
    <ul class="nav nav-pills pull-left">
	
        <li class="active"><a href="../index.html">SciPy v1.1.0.dev0+4e64658 Reference Guide</a></li>
	
          <li class="active"><a href="../stats.html" accesskey="U">Statistical functions (<code class="docutils literal"><span class="pre">scipy.stats</span></code>)</a></li> 
    </ul>
              
              
    <ul class="nav nav-pills pull-right">
      <li class="active">
        <a href="../genindex.html" title="General Index"
           accesskey="I">index</a>
      </li>
      <li class="active">
        <a href="../py-modindex.html" title="Python Module Index"
           >modules</a>
      </li>
      <li class="active">
        <a href="scipy.stats.ppcc_max.html" title="scipy.stats.ppcc_max"
           accesskey="N">next</a>
      </li>
      <li class="active">
        <a href="scipy.stats.contingency.margins.html" title="scipy.stats.contingency.margins"
           accesskey="P">previous</a>
      </li>
    </ul>
              
	    </div>
	  </div>
	</div>
        

	<div class="row-fluid">
      <div class="spc-rightsidebar span3">
        <div class="sphinxsidebarwrapper">
            <p class="logo"><a href="../index.html">
              <img class="logo" src="../_static/scipyshiny_small.png" alt="Logo">
            </a></p>
  <h4>Previous topic</h4>
  <p class="topless"><a href="scipy.stats.contingency.margins.html"
                        title="previous chapter">scipy.stats.contingency.margins</a></p>
  <h4>Next topic</h4>
  <p class="topless"><a href="scipy.stats.ppcc_max.html"
                        title="next chapter">scipy.stats.ppcc_max</a></p>


        </div>
      </div>
          <div class="span9">
            
        <div class="bodywrapper">
          <div class="body" id="spc-section-body">
            
  <div class="section" id="scipy-stats-fisher-exact">
<h1>scipy.stats.fisher_exact<a class="headerlink" href="#scipy-stats-fisher-exact" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="scipy.stats.fisher_exact">
<code class="descclassname">scipy.stats.</code><code class="descname">fisher_exact</code><span class="sig-paren">(</span><em>table</em>, <em>alternative='two-sided'</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scipy/scipy/blob/4e64658/scipy/stats/stats.py#L3018-L3175"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#scipy.stats.fisher_exact" title="Permalink to this definition">¶</a></dt>
<dd><p>Performs a Fisher exact test on a 2x2 contingency table.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>table</strong> : array_like of ints</p>
<blockquote>
<div><p>A 2x2 contingency table.  Elements should be non-negative integers.</p>
</div></blockquote>
<p><strong>alternative</strong> : {‘two-sided’, ‘less’, ‘greater’}, optional</p>
<blockquote>
<div><p>Which alternative hypothesis to the null hypothesis the test uses.
Default is ‘two-sided’.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>oddsratio</strong> : float</p>
<blockquote>
<div><p>This is prior odds ratio and not a posterior estimate.</p>
</div></blockquote>
<p><strong>p_value</strong> : float</p>
<blockquote class="last">
<div><p>P-value, the probability of obtaining a distribution at least as
extreme as the one that was actually observed, assuming that the
null hypothesis is true.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><a class="reference internal" href="scipy.stats.chi2_contingency.html#scipy.stats.chi2_contingency" title="scipy.stats.chi2_contingency"><code class="xref py py-obj docutils literal"><span class="pre">chi2_contingency</span></code></a></dt>
<dd>Chi-square test of independence of variables in a contingency table.</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>The calculated odds ratio is different from the one R uses. This scipy
implementation returns the (more common) “unconditional Maximum
Likelihood Estimate”, while R uses the “conditional Maximum Likelihood
Estimate”.</p>
<p>For tables with large numbers, the (inexact) chi-square test implemented
in the function <a class="reference internal" href="scipy.stats.chi2_contingency.html#scipy.stats.chi2_contingency" title="scipy.stats.chi2_contingency"><code class="xref py py-obj docutils literal"><span class="pre">chi2_contingency</span></code></a> can also be used.</p>
<p class="rubric">Examples</p>
<p>Say we spend a few days counting whales and sharks in the Atlantic and
Indian oceans. In the Atlantic ocean we find 8 whales and 1 shark, in the
Indian ocean 2 whales and 5 sharks. Then our contingency table is:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span>        <span class="n">Atlantic</span>  <span class="n">Indian</span>
<span class="n">whales</span>     <span class="mi">8</span>        <span class="mi">2</span>
<span class="n">sharks</span>     <span class="mi">1</span>        <span class="mi">5</span>
</pre></div>
</div>
<p>We use this table to find the p-value:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">scipy.stats</span> <span class="k">as</span> <span class="nn">stats</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">oddsratio</span><span class="p">,</span> <span class="n">pvalue</span> <span class="o">=</span> <span class="n">stats</span><span class="o">.</span><span class="n">fisher_exact</span><span class="p">([[</span><span class="mi">8</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">pvalue</span>
<span class="go">0.0349...</span>
</pre></div>
</div>
<p>The probability that we would observe this or an even more imbalanced ratio
by chance is about 3.5%.  A commonly used significance level is 5%–if we
adopt that, we can therefore conclude that our observed imbalance is
statistically significant; whales prefer the Atlantic while sharks prefer
the Indian ocean.</p>
</dd></dl>

</div>


          </div>
        </div>
          </div>
        </div>
      </div>
    </div>

    <div class="container container-navbar-bottom">
      <div class="spc-navbar">
        
      </div>
    </div>
    <div class="container">
    <div class="footer">
    <div class="row-fluid">
    <ul class="inline pull-left">
      <li>
        &copy; Copyright 2008-2016, The Scipy community.
      </li>
      <li>
      Last updated on Sep 21, 2017.
      </li>
      <li>
      Created using <a href="http://sphinx.pocoo.org/">Sphinx</a> 1.6.3.
      </li>
    </ul>
    </div>
    </div>
    </div>
  </body>
</html>