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<div class="subTitle">org.apache.commons.math3.stat.inference</div>
<h2 title="Class MannWhitneyUTest" class="title">Class MannWhitneyUTest</h2>
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<pre>public class <span class="strong">MannWhitneyUTest</span>
extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
<div class="block">An implementation of the Mann-Whitney U test (also called Wilcoxon rank-sum test).</div>
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<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/inference/MannWhitneyUTest.html#MannWhitneyUTest()">MannWhitneyUTest</a></strong>()</code>
<div class="block">Create a test instance using where NaN's are left in place and ties get
the average of applicable ranks.</div>
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<a href="../../../../../../org/apache/commons/math3/stat/ranking/TiesStrategy.html" title="enum in org.apache.commons.math3.stat.ranking">TiesStrategy</a> tiesStrategy)</code>
<div class="block">Create a test instance using the given strategies for NaN's and ties.</div>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/inference/MannWhitneyUTest.html#mannWhitneyU(double[],%20double[])">mannWhitneyU</a></strong>(double[] x,
double[] y)</code>
<div class="block">Computes the <a
href="http://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U"> Mann-Whitney
U statistic</a> comparing mean for two independent samples possibly of
different length.</div>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/inference/MannWhitneyUTest.html#mannWhitneyUTest(double[],%20double[])">mannWhitneyUTest</a></strong>(double[] x,
double[] y)</code>
<div class="block">Returns the asymptotic <i>observed significance level</i>, or <a href=
"http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#pvalue">
p-value</a>, associated with a <a
href="http://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U"> Mann-Whitney
U statistic</a> comparing mean for two independent samples.</div>
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<h4>MannWhitneyUTest</h4>
<pre>public MannWhitneyUTest()</pre>
<div class="block">Create a test instance using where NaN's are left in place and ties get
the average of applicable ranks. Use this unless you are very sure of
what you are doing.</div>
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<h4>MannWhitneyUTest</h4>
<pre>public MannWhitneyUTest(<a href="../../../../../../org/apache/commons/math3/stat/ranking/NaNStrategy.html" title="enum in org.apache.commons.math3.stat.ranking">NaNStrategy</a> nanStrategy,
<a href="../../../../../../org/apache/commons/math3/stat/ranking/TiesStrategy.html" title="enum in org.apache.commons.math3.stat.ranking">TiesStrategy</a> tiesStrategy)</pre>
<div class="block">Create a test instance using the given strategies for NaN's and ties.
Only use this if you are sure of what you are doing.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>nanStrategy</code> - specifies the strategy that should be used for Double.NaN's</dd><dd><code>tiesStrategy</code> - specifies the strategy that should be used for ties</dd></dl>
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<h4>mannWhitneyU</h4>
<pre>public double mannWhitneyU(double[] x,
double[] y)
throws <a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></pre>
<div class="block">Computes the <a
href="http://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U"> Mann-Whitney
U statistic</a> comparing mean for two independent samples possibly of
different length.
<p>
This statistic can be used to perform a Mann-Whitney U test evaluating
the null hypothesis that the two independent samples has equal mean.
</p>
<p>
Let X<sub>i</sub> denote the i'th individual of the first sample and
Y<sub>j</sub> the j'th individual in the second sample. Note that the
samples would often have different length.
</p>
<p>
<strong>Preconditions</strong>:
<ul>
<li>All observations in the two samples are independent.</li>
<li>The observations are at least ordinal (continuous are also ordinal).</li>
</ul>
</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the first sample</dd><dd><code>y</code> - the second sample</dd>
<dt><span class="strong">Returns:</span></dt><dd>Mann-Whitney U statistic (maximum of U<sup>x</sup> and U<sup>y</sup>)</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>x</code> or <code>y</code> are <code>null</code>.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if <code>x</code> or <code>y</code> are zero-length.</dd></dl>
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<h4>mannWhitneyUTest</h4>
<pre>public double mannWhitneyUTest(double[] x,
double[] y)
throws <a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</a>,
<a href="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></pre>
<div class="block">Returns the asymptotic <i>observed significance level</i>, or <a href=
"http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#pvalue">
p-value</a>, associated with a <a
href="http://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U"> Mann-Whitney
U statistic</a> comparing mean for two independent samples.
<p>
Let X<sub>i</sub> denote the i'th individual of the first sample and
Y<sub>j</sub> the j'th individual in the second sample. Note that the
samples would often have different length.
</p>
<p>
<strong>Preconditions</strong>:
<ul>
<li>All observations in the two samples are independent.</li>
<li>The observations are at least ordinal (continuous are also ordinal).</li>
</ul>
</p><p>
Ties give rise to biased variance at the moment. See e.g. <a
href="http://mlsc.lboro.ac.uk/resources/statistics/Mannwhitney.pdf"
>http://mlsc.lboro.ac.uk/resources/statistics/Mannwhitney.pdf</a>.</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the first sample</dd><dd><code>y</code> - the second sample</dd>
<dt><span class="strong">Returns:</span></dt><dd>asymptotic p-value</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>x</code> or <code>y</code> are <code>null</code>.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if <code>x</code> or <code>y</code> are zero-length.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</a></code> - if the p-value can not be computed due to a
convergence error</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - if the maximum number of iterations
is exceeded</dd></dl>
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