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<title>GNU Scientific Library &ndash; Reference Manual: Correlation</title>

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<a name="Correlation"></a>
<div class="header">
<p>
Next: <a href="Weighted-Samples.html#Weighted-Samples" accesskey="n" rel="next">Weighted Samples</a>, Previous: <a href="Covariance.html#Covariance" accesskey="p" rel="previous">Covariance</a>, Up: <a href="Statistics.html#Statistics" accesskey="u" rel="up">Statistics</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Correlation-1"></a>
<h3 class="section">21.6 Correlation</h3>
<a name="index-correlation_002c-of-two-datasets"></a>

<dl>
<dt><a name="index-gsl_005fstats_005fcorrelation"></a>Function: <em>double</em> <strong>gsl_stats_correlation</strong> <em>(const double <var>data1</var>[], const size_t <var>stride1</var>, const double <var>data2</var>[], const size_t <var>stride2</var>, const size_t <var>n</var>)</em></dt>
<dd><p>This function efficiently computes the Pearson correlation coefficient
between the datasets <var>data1</var> and <var>data2</var> which must both be of
the same length <var>n</var>.
</p><div class="example">
<pre class="example">r = cov(x, y) / (\Hat\sigma_x \Hat\sigma_y)
  = {1/(n-1) \sum (x_i - \Hat x) (y_i - \Hat y)
     \over
     \sqrt{1/(n-1) \sum (x_i - \Hat x)^2} \sqrt{1/(n-1) \sum (y_i - \Hat y)^2}
    }
</pre></div>
</dd></dl>

<dl>
<dt><a name="index-gsl_005fstats_005fspearman"></a>Function: <em>double</em> <strong>gsl_stats_spearman</strong> <em>(const double <var>data1</var>[], const size_t <var>stride1</var>, const double <var>data2</var>[], const size_t <var>stride2</var>, const size_t <var>n</var>, double <var>work</var>[])</em></dt>
<dd><p>This function computes the Spearman rank correlation coefficient between
the datasets <var>data1</var> and <var>data2</var> which must both be of the same
length <var>n</var>. Additional workspace of size 2*<var>n</var> is required in
<var>work</var>. The Spearman rank correlation between vectors <em>x</em> and
<em>y</em> is equivalent to the Pearson correlation between the ranked
vectors <em>x_R</em> and <em>y_R</em>, where ranks are defined to be the
average of the positions of an element in the ascending order of the values.
</p></dd></dl>




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