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+<div class="header">
+<div class="subTitle">org.apache.commons.math3.stat.inference</div>
+<h2 title="Class MannWhitneyUTest" class="title">Class MannWhitneyUTest</h2>
+</div>
+<div class="contentContainer">
+<ul class="inheritance">
+<li><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</a></li>
+<li>
+<ul class="inheritance">
+<li>org.apache.commons.math3.stat.inference.MannWhitneyUTest</li>
+</ul>
+</li>
+</ul>
+<div class="description">
+<ul class="blockList">
+<li class="blockList">
+<hr>
+<br>
+<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>
+</li>
+</ul>
+</div>
+<div class="summary">
+<ul class="blockList">
+<li class="blockList">
+<!-- ======== CONSTRUCTOR SUMMARY ======== -->
+<ul class="blockList">
+<li class="blockList"><a name="constructor_summary">
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+</a>
+<h3>Constructor Summary</h3>
+<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Constructor Summary table, listing constructors, and an explanation">
+<caption><span>Constructors</span><span class="tabEnd">&nbsp;</span></caption>
+<tr>
+<th class="colOne" scope="col">Constructor and Description</th>
+</tr>
+<tr class="altColor">
+<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>
+</td>
+</tr>
+<tr class="rowColor">
+<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/inference/MannWhitneyUTest.html#MannWhitneyUTest(org.apache.commons.math3.stat.ranking.NaNStrategy,%20org.apache.commons.math3.stat.ranking.TiesStrategy)">MannWhitneyUTest</a></strong>(<a href="../../../../../../org/apache/commons/math3/stat/ranking/NaNStrategy.html" title="enum in org.apache.commons.math3.stat.ranking">NaNStrategy</a>&nbsp;nanStrategy,
+ <a href="../../../../../../org/apache/commons/math3/stat/ranking/TiesStrategy.html" title="enum in org.apache.commons.math3.stat.ranking">TiesStrategy</a>&nbsp;tiesStrategy)</code>
+<div class="block">Create a test instance using the given strategies for NaN's and ties.</div>
+</td>
+</tr>
+</table>
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+</ul>
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+<h3>Method Summary</h3>
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+<caption><span>Methods</span><span class="tabEnd">&nbsp;</span></caption>
+<tr>
+<th class="colFirst" scope="col">Modifier and Type</th>
+<th class="colLast" scope="col">Method and Description</th>
+</tr>
+<tr class="altColor">
+<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[]&nbsp;x,
+ double[]&nbsp;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>
+</td>
+</tr>
+<tr class="rowColor">
+<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[]&nbsp;x,
+ double[]&nbsp;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>
+</td>
+</tr>
+</table>
+<ul class="blockList">
+<li class="blockList"><a name="methods_inherited_from_class_java.lang.Object">
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+<code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long,%20int)" title="class or interface in java.lang">wait</a></code></li>
+</ul>
+</li>
+</ul>
+</li>
+</ul>
+</div>
+<div class="details">
+<ul class="blockList">
+<li class="blockList">
+<!-- ========= CONSTRUCTOR DETAIL ======== -->
+<ul class="blockList">
+<li class="blockList"><a name="constructor_detail">
+<!-- -->
+</a>
+<h3>Constructor Detail</h3>
+<a name="MannWhitneyUTest()">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>MannWhitneyUTest</h4>
+<pre>public&nbsp;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>
+</li>
+</ul>
+<a name="MannWhitneyUTest(org.apache.commons.math3.stat.ranking.NaNStrategy, org.apache.commons.math3.stat.ranking.TiesStrategy)">
+<!-- -->
+</a>
+<ul class="blockListLast">
+<li class="blockList">
+<h4>MannWhitneyUTest</h4>
+<pre>public&nbsp;MannWhitneyUTest(<a href="../../../../../../org/apache/commons/math3/stat/ranking/NaNStrategy.html" title="enum in org.apache.commons.math3.stat.ranking">NaNStrategy</a>&nbsp;nanStrategy,
+ <a href="../../../../../../org/apache/commons/math3/stat/ranking/TiesStrategy.html" title="enum in org.apache.commons.math3.stat.ranking">TiesStrategy</a>&nbsp;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>
+</li>
+</ul>
+</li>
+</ul>
+<!-- ============ METHOD DETAIL ========== -->
+<ul class="blockList">
+<li class="blockList"><a name="method_detail">
+<!-- -->
+</a>
+<h3>Method Detail</h3>
+<a name="mannWhitneyU(double[], double[])">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>mannWhitneyU</h4>
+<pre>public&nbsp;double&nbsp;mannWhitneyU(double[]&nbsp;x,
+ double[]&nbsp;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>
+</li>
+</ul>
+<a name="mannWhitneyUTest(double[], double[])">
+<!-- -->
+</a>
+<ul class="blockListLast">
+<li class="blockList">
+<h4>mannWhitneyUTest</h4>
+<pre>public&nbsp;double&nbsp;mannWhitneyUTest(double[]&nbsp;x,
+ double[]&nbsp;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>
+</li>
+</ul>
+</li>
+</ul>
+</li>
+</ul>
+</div>
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