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| <div class="subTitle">org.apache.commons.math3.stat.inference</div> |
| <h2 title="Class GTest" class="title">Class GTest</h2> |
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| <pre>public class <span class="strong">GTest</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 <a href="http://en.wikipedia.org/wiki/G-test">G Test</a> |
| statistics. |
| |
| <p>This is known in statistical genetics as the McDonald-Kreitman test. |
| The implementation handles both known and unknown distributions.</p> |
| |
| <p>Two samples tests can be used when the distribution is unknown <i>a priori</i> |
| but provided by one sample, or when the hypothesis under test is that the two |
| samples come from the same underlying distribution.</p></div> |
| <dl><dt><span class="strong">Since:</span></dt> |
| <dd>3.1</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: GTest.java 1547633 2013-12-03 23:03:06Z tn $</dd></dl> |
| </li> |
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| <th class="colOne" scope="col">Constructor and Description</th> |
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| <td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/inference/GTest.html#GTest()">GTest</a></strong>()</code> </td> |
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| <tr class="altColor"> |
| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/inference/GTest.html#g(double[], long[])">g</a></strong>(double[] expected, |
| long[] observed)</code> |
| <div class="block">Computes the <a href="http://en.wikipedia.org/wiki/G-test">G statistic |
| for Goodness of Fit</a> comparing <code>observed</code> and <code>expected</code> |
| frequency counts.</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/GTest.html#gDataSetsComparison(long[], long[])">gDataSetsComparison</a></strong>(long[] observed1, |
| long[] observed2)</code> |
| <div class="block">Computes a G (Log-Likelihood Ratio) two sample test statistic for |
| independence comparing frequency counts in |
| <code>observed1</code> and <code>observed2</code>.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/inference/GTest.html#gTest(double[], long[])">gTest</a></strong>(double[] expected, |
| long[] observed)</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 G-Test for goodness of fit</a> comparing the |
| <code>observed</code> frequency counts to those in the <code>expected</code> array.</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/GTest.html#gTest(double[], long[], double)">gTest</a></strong>(double[] expected, |
| long[] observed, |
| double alpha)</code> |
| <div class="block">Performs a G-Test (Log-Likelihood Ratio Test) for goodness of fit |
| evaluating the null hypothesis that the observed counts conform to the |
| frequency distribution described by the expected counts, with |
| significance level <code>alpha</code>.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/inference/GTest.html#gTestDataSetsComparison(long[], long[])">gTestDataSetsComparison</a></strong>(long[] observed1, |
| long[] observed2)</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 G-Value (Log-Likelihood Ratio) for two |
| sample test comparing bin frequency counts in <code>observed1</code> and |
| <code>observed2</code>.</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/GTest.html#gTestDataSetsComparison(long[], long[], double)">gTestDataSetsComparison</a></strong>(long[] observed1, |
| long[] observed2, |
| double alpha)</code> |
| <div class="block">Performs a G-Test (Log-Likelihood Ratio Test) comparing two binned |
| data sets.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/inference/GTest.html#gTestIntrinsic(double[], long[])">gTestIntrinsic</a></strong>(double[] expected, |
| long[] observed)</code> |
| <div class="block">Returns the intrinsic (Hardy-Weinberg proportions) p-Value, as described |
| in p64-69 of McDonald, J.H.</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/GTest.html#rootLogLikelihoodRatio(long, long, long, long)">rootLogLikelihoodRatio</a></strong>(long k11, |
| long k12, |
| long k21, |
| long k22)</code> |
| <div class="block">Calculates the root log-likelihood ratio for 2 state Datasets.</div> |
| </td> |
| </tr> |
| </table> |
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| <code><a href="http://docs.oracle.com/javase/6/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/6/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/6/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/6/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/6/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/6/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/6/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/6/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/6/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/6/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/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</a></code></li> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| </div> |
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| <ul class="blockList"> |
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| <!-- ========= CONSTRUCTOR DETAIL ======== --> |
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| <a name="GTest()"> |
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| <li class="blockList"> |
| <h4>GTest</h4> |
| <pre>public GTest()</pre> |
| </li> |
| </ul> |
| </li> |
| </ul> |
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| <a name="g(double[], long[])"> |
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| <h4>g</h4> |
| <pre>public double g(double[] expected, |
| long[] observed) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></pre> |
| <div class="block">Computes the <a href="http://en.wikipedia.org/wiki/G-test">G statistic |
| for Goodness of Fit</a> comparing <code>observed</code> and <code>expected</code> |
| frequency counts. |
| |
| <p>This statistic can be used to perform a G test (Log-Likelihood Ratio |
| Test) evaluating the null hypothesis that the observed counts follow the |
| expected distribution.</p> |
| |
| <p><strong>Preconditions</strong>: <ul> |
| <li>Expected counts must all be positive. </li> |
| <li>Observed counts must all be ≥ 0. </li> |
| <li>The observed and expected arrays must have the same length and their |
| common length must be at least 2. </li></ul></p> |
| |
| <p>If any of the preconditions are not met, a |
| <code>MathIllegalArgumentException</code> is thrown.</p> |
| |
| <p><strong>Note:</strong>This implementation rescales the |
| <code>expected</code> array if necessary to ensure that the sum of the |
| expected and observed counts are equal.</p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>observed</code> - array of observed frequency counts</dd><dd><code>expected</code> - array of expected frequency counts</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>G-Test statistic</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>observed</code> has negative entries</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></code> - if <code>expected</code> has entries that |
| are not strictly positive</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the array lengths do not match or |
| are less than 2.</dd></dl> |
| </li> |
| </ul> |
| <a name="gTest(double[], long[])"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>gTest</h4> |
| <pre>public double gTest(double[] expected, |
| long[] observed) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</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 <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 G-Test for goodness of fit</a> comparing the |
| <code>observed</code> frequency counts to those in the <code>expected</code> array. |
| |
| <p>The number returned is the smallest significance level at which one |
| can reject the null hypothesis that the observed counts conform to the |
| frequency distribution described by the expected counts.</p> |
| |
| <p>The probability returned is the tail probability beyond |
| <a href="../../../../../../org/apache/commons/math3/stat/inference/GTest.html#g(double[], long[])"><code>g(expected, observed)</code></a> |
| in the ChiSquare distribution with degrees of freedom one less than the |
| common length of <code>expected</code> and <code>observed</code>.</p> |
| |
| <p> <strong>Preconditions</strong>: <ul> |
| <li>Expected counts must all be positive. </li> |
| <li>Observed counts must all be ≥ 0. </li> |
| <li>The observed and expected arrays must have the |
| same length and their common length must be at least 2.</li> |
| </ul></p> |
| |
| <p>If any of the preconditions are not met, a |
| <code>MathIllegalArgumentException</code> is thrown.</p> |
| |
| <p><strong>Note:</strong>This implementation rescales the |
| <code>expected</code> array if necessary to ensure that the sum of the |
| expected and observed counts are equal.</p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>observed</code> - array of observed frequency counts</dd><dd><code>expected</code> - array of expected frequency counts</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>observed</code> has negative entries</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></code> - if <code>expected</code> has entries that |
| are not strictly positive</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the array lengths do not match or |
| are less than 2.</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - if an error occurs computing the |
| p-value.</dd></dl> |
| </li> |
| </ul> |
| <a name="gTestIntrinsic(double[], long[])"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>gTestIntrinsic</h4> |
| <pre>public double gTestIntrinsic(double[] expected, |
| long[] observed) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</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 intrinsic (Hardy-Weinberg proportions) p-Value, as described |
| in p64-69 of McDonald, J.H. 2009. Handbook of Biological Statistics |
| (2nd ed.). Sparky House Publishing, Baltimore, Maryland. |
| |
| <p> The probability returned is the tail probability beyond |
| <a href="../../../../../../org/apache/commons/math3/stat/inference/GTest.html#g(double[], long[])"><code>g(expected, observed)</code></a> |
| in the ChiSquare distribution with degrees of freedom two less than the |
| common length of <code>expected</code> and <code>observed</code>.</p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>observed</code> - array of observed frequency counts</dd><dd><code>expected</code> - array of expected frequency counts</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>observed</code> has negative entries</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></code> - <code>expected</code> has entries that are |
| not strictly positive</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the array lengths do not match or |
| are less than 2.</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - if an error occurs computing the |
| p-value.</dd></dl> |
| </li> |
| </ul> |
| <a name="gTest(double[], long[], double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>gTest</h4> |
| <pre>public boolean gTest(double[] expected, |
| long[] observed, |
| double alpha) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></pre> |
| <div class="block">Performs a G-Test (Log-Likelihood Ratio Test) for goodness of fit |
| evaluating the null hypothesis that the observed counts conform to the |
| frequency distribution described by the expected counts, with |
| significance level <code>alpha</code>. Returns true iff the null |
| hypothesis can be rejected with <code>100 * (1 - alpha)</code> percent confidence. |
| |
| <p><strong>Example:</strong><br> To test the hypothesis that |
| <code>observed</code> follows <code>expected</code> at the 99% level, |
| use </p><p> |
| <code>gTest(expected, observed, 0.01)</code></p> |
| |
| <p>Returns true iff <a href="../../../../../../org/apache/commons/math3/stat/inference/GTest.html#gTest(double[], long[])"><code>gTestGoodnessOfFitPValue(expected, observed)</code></a> < alpha</p> |
| |
| <p><strong>Preconditions</strong>: <ul> |
| <li>Expected counts must all be positive. </li> |
| <li>Observed counts must all be ≥ 0. </li> |
| <li>The observed and expected arrays must have the same length and their |
| common length must be at least 2. |
| <li> <code>0 < alpha < 0.5</code> </li></ul></p> |
| |
| <p>If any of the preconditions are not met, a |
| <code>MathIllegalArgumentException</code> is thrown.</p> |
| |
| <p><strong>Note:</strong>This implementation rescales the |
| <code>expected</code> array if necessary to ensure that the sum of the |
| expected and observed counts are equal.</p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>observed</code> - array of observed frequency counts</dd><dd><code>expected</code> - array of expected frequency counts</dd><dd><code>alpha</code> - significance level of the test</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>true iff null hypothesis can be rejected with confidence 1 - |
| alpha</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>observed</code> has negative entries</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></code> - if <code>expected</code> has entries that |
| are not strictly positive</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the array lengths do not match or |
| are less than 2.</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - if an error occurs computing the |
| p-value.</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></code> - if alpha is not strictly greater than zero |
| and less than or equal to 0.5</dd></dl> |
| </li> |
| </ul> |
| <a name="gDataSetsComparison(long[], long[])"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>gDataSetsComparison</h4> |
| <pre>public double gDataSetsComparison(long[] observed1, |
| long[] observed2) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</a></pre> |
| <div class="block"><p>Computes a G (Log-Likelihood Ratio) two sample test statistic for |
| independence comparing frequency counts in |
| <code>observed1</code> and <code>observed2</code>. The sums of frequency |
| counts in the two samples are not required to be the same. The formula |
| used to compute the test statistic is </p> |
| |
| <p><code>2 * totalSum * [H(rowSums) + H(colSums) - H(k)]</code></p> |
| |
| <p> where <code>H</code> is the |
| <a href="http://en.wikipedia.org/wiki/Entropy_%28information_theory%29"> |
| Shannon Entropy</a> of the random variable formed by viewing the elements |
| of the argument array as incidence counts; <br/> |
| <code>k</code> is a matrix with rows <code>[observed1, observed2]</code>; <br/> |
| <code>rowSums, colSums</code> are the row/col sums of <code>k</code>; <br> |
| and <code>totalSum</code> is the overall sum of all entries in <code>k</code>.</p> |
| |
| <p>This statistic can be used to perform a G test evaluating the null |
| hypothesis that both observed counts are independent </p> |
| |
| <p> <strong>Preconditions</strong>: <ul> |
| <li>Observed counts must be non-negative. </li> |
| <li>Observed counts for a specific bin must not both be zero. </li> |
| <li>Observed counts for a specific sample must not all be 0. </li> |
| <li>The arrays <code>observed1</code> and <code>observed2</code> must have |
| the same length and their common length must be at least 2. </li></ul></p> |
| |
| <p>If any of the preconditions are not met, a |
| <code>MathIllegalArgumentException</code> is thrown.</p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>observed1</code> - array of observed frequency counts of the first data set</dd><dd><code>observed2</code> - array of observed frequency counts of the second data |
| set</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>G-Test statistic</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - the the lengths of the arrays do not |
| match or their common length is less than 2</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if any entry in <code>observed1</code> or |
| <code>observed2</code> is negative</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</a></code> - if either all counts of |
| <code>observed1</code> or <code>observed2</code> are zero, or if the count |
| at the same index is zero for both arrays.</dd></dl> |
| </li> |
| </ul> |
| <a name="rootLogLikelihoodRatio(long, long, long, long)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>rootLogLikelihoodRatio</h4> |
| <pre>public double rootLogLikelihoodRatio(long k11, |
| long k12, |
| long k21, |
| long k22)</pre> |
| <div class="block">Calculates the root log-likelihood ratio for 2 state Datasets. See |
| <a href="../../../../../../org/apache/commons/math3/stat/inference/GTest.html#gDataSetsComparison(long[], long[])"><code>gDataSetsComparison(long[], long[] )</code></a>. |
| |
| <p>Given two events A and B, let k11 be the number of times both events |
| occur, k12 the incidence of B without A, k21 the count of A without B, |
| and k22 the number of times neither A nor B occurs. What is returned |
| by this method is </p> |
| |
| <p><code>(sgn) sqrt(gValueDataSetsComparison({k11, k12}, {k21, k22})</code></p> |
| |
| <p>where <code>sgn</code> is -1 if <code>k11 / (k11 + k12) < k21 / (k21 + k22))</code>;<br/> |
| 1 otherwise.</p> |
| |
| <p>Signed root LLR has two advantages over the basic LLR: a) it is positive |
| where k11 is bigger than expected, negative where it is lower b) if there is |
| no difference it is asymptotically normally distributed. This allows one |
| to talk about "number of standard deviations" which is a more common frame |
| of reference than the chi^2 distribution.</p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>k11</code> - number of times the two events occurred together (AB)</dd><dd><code>k12</code> - number of times the second event occurred WITHOUT the |
| first event (notA,B)</dd><dd><code>k21</code> - number of times the first event occurred WITHOUT the |
| second event (A, notB)</dd><dd><code>k22</code> - number of times something else occurred (i.e. was neither |
| of these events (notA, notB)</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>root log-likelihood ratio</dd></dl> |
| </li> |
| </ul> |
| <a name="gTestDataSetsComparison(long[], long[])"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>gTestDataSetsComparison</h4> |
| <pre>public double gTestDataSetsComparison(long[] observed1, |
| long[] observed2) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></pre> |
| <div class="block"><p>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 G-Value (Log-Likelihood Ratio) for two |
| sample test comparing bin frequency counts in <code>observed1</code> and |
| <code>observed2</code>.</p> |
| |
| <p>The number returned is the smallest significance level at which one |
| can reject the null hypothesis that the observed counts conform to the |
| same distribution. </p> |
| |
| <p>See <a href="../../../../../../org/apache/commons/math3/stat/inference/GTest.html#gTest(double[], long[])"><code>gTest(double[], long[])</code></a> for details |
| on how the p-value is computed. The degrees of of freedom used to |
| perform the test is one less than the common length of the input observed |
| count arrays.</p> |
| |
| <p><strong>Preconditions</strong>: |
| <ul> <li>Observed counts must be non-negative. </li> |
| <li>Observed counts for a specific bin must not both be zero. </li> |
| <li>Observed counts for a specific sample must not all be 0. </li> |
| <li>The arrays <code>observed1</code> and <code>observed2</code> must |
| have the same length and their common length must be at least 2. </li> |
| </ul><p> |
| <p> If any of the preconditions are not met, a |
| <code>MathIllegalArgumentException</code> is thrown.</p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>observed1</code> - array of observed frequency counts of the first data set</dd><dd><code>observed2</code> - array of observed frequency counts of the second data |
| set</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/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - the the length of the arrays does not |
| match or their common length is less than 2</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if any of the entries in <code>observed1</code> or |
| <code>observed2</code> are negative</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</a></code> - if either all counts of <code>observed1</code> or |
| <code>observed2</code> are zero, or if the count at some index is |
| zero for both arrays</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - if an error occurs computing the |
| p-value.</dd></dl> |
| </li> |
| </ul> |
| <a name="gTestDataSetsComparison(long[], long[], double)"> |
| <!-- --> |
| </a> |
| <ul class="blockListLast"> |
| <li class="blockList"> |
| <h4>gTestDataSetsComparison</h4> |
| <pre>public boolean gTestDataSetsComparison(long[] observed1, |
| long[] observed2, |
| double alpha) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></pre> |
| <div class="block"><p>Performs a G-Test (Log-Likelihood Ratio Test) comparing two binned |
| data sets. The test evaluates the null hypothesis that the two lists |
| of observed counts conform to the same frequency distribution, with |
| significance level <code>alpha</code>. Returns true iff the null |
| hypothesis can be rejected with 100 * (1 - alpha) percent confidence. |
| </p> |
| <p>See <a href="../../../../../../org/apache/commons/math3/stat/inference/GTest.html#gDataSetsComparison(long[], long[])"><code>gDataSetsComparison(long[], long[])</code></a> for details |
| on the formula used to compute the G (LLR) statistic used in the test and |
| <a href="../../../../../../org/apache/commons/math3/stat/inference/GTest.html#gTest(double[], long[])"><code>gTest(double[], long[])</code></a> for information on how |
| the observed significance level is computed. The degrees of of freedom used |
| to perform the test is one less than the common length of the input observed |
| count arrays. </p> |
| |
| <strong>Preconditions</strong>: <ul> |
| <li>Observed counts must be non-negative. </li> |
| <li>Observed counts for a specific bin must not both be zero. </li> |
| <li>Observed counts for a specific sample must not all be 0. </li> |
| <li>The arrays <code>observed1</code> and <code>observed2</code> must |
| have the same length and their common length must be at least 2. </li> |
| <li><code>0 < alpha < 0.5</code> </li></ul></p> |
| |
| <p>If any of the preconditions are not met, a |
| <code>MathIllegalArgumentException</code> is thrown.</p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>observed1</code> - array of observed frequency counts of the first data set</dd><dd><code>observed2</code> - array of observed frequency counts of the second data |
| set</dd><dd><code>alpha</code> - significance level of the test</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>true iff null hypothesis can be rejected with confidence 1 - |
| alpha</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - the the length of the arrays does not |
| match</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if any of the entries in <code>observed1</code> or |
| <code>observed2</code> are negative</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</a></code> - if either all counts of <code>observed1</code> or |
| <code>observed2</code> are zero, or if the count at some index is |
| zero for both arrays</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>alpha</code> is not in the range |
| (0, 0.5]</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - if an error occurs performing the test</dd></dl> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| </ul> |
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