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| <h2 title="Class ChiSquareTest" class="title">Class ChiSquareTest</h2> |
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| <pre>public class <span class="strong">ChiSquareTest</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 Chi-Square test statistics. |
| |
| <p>This 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">Version:</span></dt> |
| <dd>$Id: ChiSquareTest.java 1416643 2012-12-03 19:37:14Z tn $</dd></dl> |
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| <th class="colOne" scope="col">Constructor and Description</th> |
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| <tr class="altColor"> |
| <td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/inference/ChiSquareTest.html#ChiSquareTest()">ChiSquareTest</a></strong>()</code> |
| <div class="block">Construct a ChiSquareTest</div> |
| </td> |
| </tr> |
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| <th class="colLast" scope="col">Method and Description</th> |
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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/ChiSquareTest.html#chiSquare(double[], long[])">chiSquare</a></strong>(double[] expected, |
| long[] observed)</code> |
| <div class="block">Computes the <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm"> |
| Chi-Square statistic</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/ChiSquareTest.html#chiSquare(long[][])">chiSquare</a></strong>(long[][] counts)</code> |
| <div class="block">Computes the Chi-Square statistic associated with a |
| <a href="http://www.itl.nist.gov/div898/handbook/prc/section4/prc45.htm"> |
| chi-square test of independence</a> based on the input <code>counts</code> |
| array, viewed as a two-way table.</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/ChiSquareTest.html#chiSquareDataSetsComparison(long[], long[])">chiSquareDataSetsComparison</a></strong>(long[] observed1, |
| long[] observed2)</code> |
| <div class="block">Computes a |
| <a href="http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/chi2samp.htm"> |
| Chi-Square two sample test statistic</a> comparing bin frequency counts |
| in <code>observed1</code> and <code>observed2</code>.</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/ChiSquareTest.html#chiSquareTest(double[], long[])">chiSquareTest</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 |
| <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm"> |
| Chi-square goodness of fit test</a> comparing the <code>observed</code> |
| frequency counts to those in the <code>expected</code> array.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>boolean</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/inference/ChiSquareTest.html#chiSquareTest(double[], long[], double)">chiSquareTest</a></strong>(double[] expected, |
| long[] observed, |
| double alpha)</code> |
| <div class="block">Performs a <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm"> |
| Chi-square goodness of fit test</a> 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="rowColor"> |
| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/inference/ChiSquareTest.html#chiSquareTest(long[][])">chiSquareTest</a></strong>(long[][] counts)</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://www.itl.nist.gov/div898/handbook/prc/section4/prc45.htm"> |
| chi-square test of independence</a> based on the input <code>counts</code> |
| array, viewed as a two-way table.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>boolean</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/inference/ChiSquareTest.html#chiSquareTest(long[][], double)">chiSquareTest</a></strong>(long[][] counts, |
| double alpha)</code> |
| <div class="block">Performs a <a href="http://www.itl.nist.gov/div898/handbook/prc/section4/prc45.htm"> |
| chi-square test of independence</a> evaluating the null hypothesis that the |
| classifications represented by the counts in the columns of the input 2-way table |
| are independent of the rows, with significance level <code>alpha</code>.</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/ChiSquareTest.html#chiSquareTestDataSetsComparison(long[], long[])">chiSquareTestDataSetsComparison</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 Chi-Square two sample test comparing |
| bin frequency counts in <code>observed1</code> and |
| <code>observed2</code>.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>boolean</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/inference/ChiSquareTest.html#chiSquareTestDataSetsComparison(long[], long[], double)">chiSquareTestDataSetsComparison</a></strong>(long[] observed1, |
| long[] observed2, |
| double alpha)</code> |
| <div class="block">Performs a Chi-Square two sample test comparing two binned data |
| sets.</div> |
| </td> |
| </tr> |
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| </ul> |
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| </ul> |
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| </ul> |
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| <div class="details"> |
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| <!-- ========= CONSTRUCTOR DETAIL ======== --> |
| <ul class="blockList"> |
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| <a name="ChiSquareTest()"> |
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| </a> |
| <ul class="blockListLast"> |
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| <h4>ChiSquareTest</h4> |
| <pre>public ChiSquareTest()</pre> |
| <div class="block">Construct a ChiSquareTest</div> |
| </li> |
| </ul> |
| </li> |
| </ul> |
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| <li class="blockList"><a name="method_detail"> |
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| <a name="chiSquare(double[], long[])"> |
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| <h4>chiSquare</h4> |
| <pre>public double chiSquare(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://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm"> |
| Chi-Square statistic</a> comparing <code>observed</code> and <code>expected</code> |
| frequency counts. |
| <p> |
| This statistic can be used to perform a Chi-Square 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, an |
| <code>IllegalArgumentException</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>chiSquare 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 arrays length is less than 2</dd></dl> |
| </li> |
| </ul> |
| <a name="chiSquareTest(double[], long[])"> |
| <!-- --> |
| </a> |
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| <h4>chiSquareTest</h4> |
| <pre>public double chiSquareTest(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 |
| <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm"> |
| Chi-square goodness of fit test</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> |
| <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, an |
| <code>IllegalArgumentException</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 arrays length is 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="chiSquareTest(double[], long[], double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>chiSquareTest</h4> |
| <pre>public boolean chiSquareTest(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 <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm"> |
| Chi-square goodness of fit test</a> 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 100 * (1 - alpha) 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>chiSquareTest(expected, observed, 0.01) </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> <code> 0 < alpha < 0.5 </code> |
| </li></ul></p><p> |
| If any of the preconditions are not met, an |
| <code>IllegalArgumentException</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 arrays length is less than 2</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 computing the p-value</dd></dl> |
| </li> |
| </ul> |
| <a name="chiSquare(long[][])"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>chiSquare</h4> |
| <pre>public double chiSquare(long[][] counts) |
| 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/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</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 Chi-Square statistic associated with a |
| <a href="http://www.itl.nist.gov/div898/handbook/prc/section4/prc45.htm"> |
| chi-square test of independence</a> based on the input <code>counts</code> |
| array, viewed as a two-way table. |
| <p> |
| The rows of the 2-way table are |
| <code>count[0], ... , count[count.length - 1] </code></p> |
| <p> |
| <strong>Preconditions</strong>: <ul> |
| <li>All counts must be ≥ 0. |
| </li> |
| <li>The count array must be rectangular (i.e. all count[i] subarrays |
| must have the same length). |
| </li> |
| <li>The 2-way table represented by <code>counts</code> must have at |
| least 2 columns and at least 2 rows. |
| </li> |
| </li></ul></p><p> |
| If any of the preconditions are not met, an |
| <code>IllegalArgumentException</code> is thrown.</p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>counts</code> - array representation of 2-way table</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>chiSquare test statistic</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 the array is null</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 is not rectangular</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if <code>counts</code> has negative entries</dd></dl> |
| </li> |
| </ul> |
| <a name="chiSquareTest(long[][])"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>chiSquareTest</h4> |
| <pre>public double chiSquareTest(long[][] counts) |
| 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/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/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 |
| <a href="http://www.itl.nist.gov/div898/handbook/prc/section4/prc45.htm"> |
| chi-square test of independence</a> based on the input <code>counts</code> |
| array, viewed as a two-way table. |
| <p> |
| The rows of the 2-way table are |
| <code>count[0], ... , count[count.length - 1] </code></p> |
| <p> |
| <strong>Preconditions</strong>: <ul> |
| <li>All counts must be ≥ 0. |
| </li> |
| <li>The count array must be rectangular (i.e. all count[i] subarrays must have |
| the same length). |
| </li> |
| <li>The 2-way table represented by <code>counts</code> must have at least 2 |
| columns and at least 2 rows. |
| </li> |
| </li></ul></p><p> |
| If any of the preconditions are not met, an |
| <code>IllegalArgumentException</code> is thrown.</p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>counts</code> - array representation of 2-way table</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/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if the array is null</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 is not rectangular</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if <code>counts</code> has negative entries</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="chiSquareTest(long[][], double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>chiSquareTest</h4> |
| <pre>public boolean chiSquareTest(long[][] counts, |
| double alpha) |
| 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/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/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 <a href="http://www.itl.nist.gov/div898/handbook/prc/section4/prc45.htm"> |
| chi-square test of independence</a> evaluating the null hypothesis that the |
| classifications represented by the counts in the columns of the input 2-way table |
| are independent of the rows, with significance level <code>alpha</code>. |
| Returns true iff the null hypothesis can be rejected with 100 * (1 - alpha) percent |
| confidence. |
| <p> |
| The rows of the 2-way table are |
| <code>count[0], ... , count[count.length - 1] </code></p> |
| <p> |
| <strong>Example:</strong><br> |
| To test the null hypothesis that the counts in |
| <code>count[0], ... , count[count.length - 1] </code> |
| all correspond to the same underlying probability distribution at the 99% level, use</p> |
| <p><code>chiSquareTest(counts, 0.01)</code></p> |
| <p> |
| <strong>Preconditions</strong>: <ul> |
| <li>All counts must be ≥ 0. |
| </li> |
| <li>The count array must be rectangular (i.e. all count[i] subarrays must have the |
| same length).</li> |
| <li>The 2-way table represented by <code>counts</code> must have at least 2 columns and |
| at least 2 rows.</li> |
| </li></ul></p><p> |
| If any of the preconditions are not met, an |
| <code>IllegalArgumentException</code> is thrown.</p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>counts</code> - array representation of 2-way table</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/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if the array is null</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 is not rectangular</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</a></code> - if <code>counts</code> has any negative entries</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 computing the p-value</dd></dl> |
| </li> |
| </ul> |
| <a name="chiSquareDataSetsComparison(long[], long[])"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>chiSquareDataSetsComparison</h4> |
| <pre>public double chiSquareDataSetsComparison(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 |
| <a href="http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/chi2samp.htm"> |
| Chi-Square two sample test statistic</a> comparing bin 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> |
| <code> |
| ∑[(K * observed1[i] - observed2[i]/K)<sup>2</sup> / (observed1[i] + observed2[i])] |
| </code> where |
| <br/><code>K = &sqrt;[&sum(observed2 / ∑(observed1)]</code> |
| </p> |
| <p>This statistic can be used to perform a Chi-Square test evaluating the |
| null hypothesis that both observed counts follow the same distribution.</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, an |
| <code>IllegalArgumentException</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>chiSquare 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 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 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><dt><span class="strong">Since:</span></dt> |
| <dd>1.2</dd></dl> |
| </li> |
| </ul> |
| <a name="chiSquareTestDataSetsComparison(long[], long[])"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>chiSquareTestDataSetsComparison</h4> |
| <pre>public double chiSquareTestDataSetsComparison(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 Chi-Square 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/ChiSquareTest.html#chiSquareDataSetsComparison(long[], long[])"><code>chiSquareDataSetsComparison(long[], long[])</code></a> for details |
| on the formula used to compute the test statistic. 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></ul><p> |
| If any of the preconditions are not met, an |
| <code>IllegalArgumentException</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</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 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 the same 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><dt><span class="strong">Since:</span></dt> |
| <dd>1.2</dd></dl> |
| </li> |
| </ul> |
| <a name="chiSquareTestDataSetsComparison(long[], long[], double)"> |
| <!-- --> |
| </a> |
| <ul class="blockListLast"> |
| <li class="blockList"> |
| <h4>chiSquareTestDataSetsComparison</h4> |
| <pre>public boolean chiSquareTestDataSetsComparison(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 Chi-Square two sample 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/ChiSquareTest.html#chiSquareDataSetsComparison(long[], long[])"><code>chiSquareDataSetsComparison(long[], long[])</code></a> for |
| details on the formula used to compute the Chisquare statistic used |
| in the test. 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> |
| If any of the preconditions are not met, an |
| <code>IllegalArgumentException</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 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 the same 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><dt><span class="strong">Since:</span></dt> |
| <dd>1.2</dd></dl> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| </div> |
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