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| <div class="subTitle">org.apache.commons.math3.stat.inference</div> |
| <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/6/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">Version:</span></dt> |
| <dd>$Id: BinomialTest.java 1532638 2013-10-16 04:29:31Z psteitz $</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, int, double, org.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> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>boolean</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/inference/BinomialTest.html#binomialTest(int, int, double, org.apache.commons.math3.stat.inference.AlternativeHypothesis, double)">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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| <h4>BinomialTest</h4> |
| <pre>public BinomialTest()</pre> |
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| <h4>binomialTest</h4> |
| <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> |
| </li> |
| </ul> |
| <a name="binomialTest(int, int, double, org.apache.commons.math3.stat.inference.AlternativeHypothesis)"> |
| <!-- --> |
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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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