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<h2 title="Class BinomialTest" class="title">Class BinomialTest</h2>
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<pre>public class <span class="strong">BinomialTest</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">Implements binomial test statistics.
<p>
Exact test for the statistical significance of deviations from a
theoretically expected distribution of observations into two categories.</div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>3.3</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="http://en.wikipedia.org/wiki/Binomial_test">Binomial test (Wikipedia)</a></dd></dl>
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<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/inference/BinomialTest.html#BinomialTest()">BinomialTest</a></strong>()</code> </td>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/inference/BinomialTest.html#binomialTest(int,%20int,%20double,%20org.apache.commons.math3.stat.inference.AlternativeHypothesis)">binomialTest</a></strong>(int numberOfTrials,
int numberOfSuccesses,
double probability,
<a href="../../../../../../org/apache/commons/math3/stat/inference/AlternativeHypothesis.html" title="enum in org.apache.commons.math3.stat.inference">AlternativeHypothesis</a> alternativeHypothesis)</code>
<div class="block">Returns the <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/Binomial_test"> Binomial test</a>.</div>
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<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/inference/BinomialTest.html#binomialTest(int,%20int,%20double,%20org.apache.commons.math3.stat.inference.AlternativeHypothesis,%20double)">binomialTest</a></strong>(int numberOfTrials,
int numberOfSuccesses,
double probability,
<a href="../../../../../../org/apache/commons/math3/stat/inference/AlternativeHypothesis.html" title="enum in org.apache.commons.math3.stat.inference">AlternativeHypothesis</a> alternativeHypothesis,
double alpha)</code>
<div class="block">Returns whether the null hypothesis can be rejected with the given confidence level.</div>
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<pre>public BinomialTest()</pre>
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<pre>public boolean binomialTest(int numberOfTrials,
int numberOfSuccesses,
double probability,
<a href="../../../../../../org/apache/commons/math3/stat/inference/AlternativeHypothesis.html" title="enum in org.apache.commons.math3.stat.inference">AlternativeHypothesis</a> alternativeHypothesis,
double alpha)</pre>
<div class="block">Returns whether the null hypothesis can be rejected with the given confidence level.
<p>
<strong>Preconditions</strong>:
<ul>
<li>Number of trials must be ≥ 0.</li>
<li>Number of successes must be ≥ 0.</li>
<li>Number of successes must be ≤ number of trials.</li>
<li>Probability must be ≥ 0 and ≤ 1.</li>
</ul></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>numberOfTrials</code> - number of trials performed</dd><dd><code>numberOfSuccesses</code> - number of successes observed</dd><dd><code>probability</code> - assumed probability of a single trial under the null hypothesis</dd><dd><code>alternativeHypothesis</code> - type of hypothesis being evaluated (one- or two-sided)</dd><dd><code>alpha</code> - significance level of the test</dd>
<dt><span class="strong">Returns:</span></dt><dd>true if the null hypothesis can be rejected with confidence <code>1 - alpha</code></dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if <code>numberOfTrials</code> or <code>numberOfSuccesses</code> is negative</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></code> - if <code>probability</code> is not between 0 and 1</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if <code>numberOfTrials</code> < <code>numberOfSuccesses</code> or
if <code>alternateHypothesis</code> is null.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/stat/inference/AlternativeHypothesis.html" title="enum in org.apache.commons.math3.stat.inference"><code>AlternativeHypothesis</code></a></dd></dl>
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<h4>binomialTest</h4>
<pre>public double binomialTest(int numberOfTrials,
int numberOfSuccesses,
double probability,
<a href="../../../../../../org/apache/commons/math3/stat/inference/AlternativeHypothesis.html" title="enum in org.apache.commons.math3.stat.inference">AlternativeHypothesis</a> alternativeHypothesis)</pre>
<div class="block">Returns the <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/Binomial_test"> Binomial test</a>.
<p>
The number returned is the smallest significance level at which one can reject the null hypothesis.
The form of the hypothesis depends on <code>alternativeHypothesis</code>.</p>
<p>
The p-Value represents the likelihood of getting a result at least as extreme as the sample,
given the provided <code>probability</code> of success on a single trial. For single-sided tests,
this value can be directly derived from the Binomial distribution. For the two-sided test,
the implementation works as follows: we start by looking at the most extreme cases
(0 success and n success where n is the number of trials from the sample) and determine their likelihood.
The lower value is added to the p-Value (if both values are equal, both are added). Then we continue with
the next extreme value, until we added the value for the actual observed sample.</p>
<p>
<strong>Preconditions</strong>:
<ul>
<li>Number of trials must be ≥ 0.</li>
<li>Number of successes must be ≥ 0.</li>
<li>Number of successes must be ≤ number of trials.</li>
<li>Probability must be ≥ 0 and ≤ 1.</li>
</ul></p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>numberOfTrials</code> - number of trials performed</dd><dd><code>numberOfSuccesses</code> - number of successes observed</dd><dd><code>probability</code> - assumed probability of a single trial under the null hypothesis</dd><dd><code>alternativeHypothesis</code> - type of hypothesis being evaluated (one- or two-sided)</dd>
<dt><span class="strong">Returns:</span></dt><dd>p-value</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if <code>numberOfTrials</code> or <code>numberOfSuccesses</code> is negative</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></code> - if <code>probability</code> is not between 0 and 1</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if <code>numberOfTrials</code> < <code>numberOfSuccesses</code> or
if <code>alternateHypothesis</code> is null.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/stat/inference/AlternativeHypothesis.html" title="enum in org.apache.commons.math3.stat.inference"><code>AlternativeHypothesis</code></a></dd></dl>
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