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<div class="subTitle">edu.rit.numeric</div>
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<h2 title="Class Statistics" class="title">Class Statistics</h2>
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<div class="contentContainer">
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<ul class="inheritance">
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<li><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</a></li>
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<pre>public class <span class="strong">Statistics</span>
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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>
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<div class="block">Class Statistics provides static methods for doing statistical tests.
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<P>
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For each statistical test, there is a method that returns the "p-value" of
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the test statistic. This is the probability that the test statistic would
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have a value greater than or equal to the observed value if the null
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hypothesis is true.</div>
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<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation">
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<caption><span>Methods</span><span class="tabEnd"> </span></caption>
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<tr>
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<th class="colFirst" scope="col">Modifier and Type</th>
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<th class="colLast" scope="col">Method and Description</th>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Statistics.html#bernoulliChiSquarePvalue(double)">bernoulliChiSquarePvalue</a></strong>(double chisqr)</code>
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<div class="block">Returns the p-value of a Bernoulli chi-square statistic.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Statistics.html#bernoulliChiSquareTest(long, long)">bernoulliChiSquareTest</a></strong>(long total,
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long measured)</code>
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<div class="block">Do a Bernoulli chi-square test on the given data.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Statistics.html#chiSquarePvalue(double, double)">chiSquarePvalue</a></strong>(double N,
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double chisqr)</code>
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<div class="block">Returns the p-value of a chi-square statistic.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Statistics.html#chiSquareTest(double[], double[])">chiSquareTest</a></strong>(double[] measured,
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double[] expected)</code>
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<div class="block">Do a chi-square test on the given data.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Statistics.html#ksPvalue(double, double)">ksPvalue</a></strong>(double N,
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double D)</code>
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<div class="block">Returns the p-value of a K-S statistic.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Statistics.html#ksTest(double[])">ksTest</a></strong>(double[] data)</code>
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<div class="block">Do a Kolmogorov-Smirnov (K-S) test on the given data.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Statistics.html#ksTest(double[], edu.rit.numeric.Function)">ksTest</a></strong>(double[] data,
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<a href="../../../edu/rit/numeric/Function.html" title="interface in edu.rit.numeric">Function</a> cdf)</code>
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<div class="block">Do a Kolmogorov-Smirnov (K-S) test on the given data.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Statistics.html#normalPvalue(double, double, double)">normalPvalue</a></strong>(double x,
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double mean,
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double stddev)</code>
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<div class="block">Returns the p-value of a statistic drawn from a normal distribution.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>static double[]</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Statistics.html#tTestUnequalVariance(edu.rit.numeric.Series, edu.rit.numeric.Series)">tTestUnequalVariance</a></strong>(<a href="../../../edu/rit/numeric/Series.html" title="class in edu.rit.numeric">Series</a> data1,
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<a href="../../../edu/rit/numeric/Series.html" title="class in edu.rit.numeric">Series</a> data2)</code>
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<div class="block">Do an unequal-variance <I>t</I>-test on the two given data series.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Statistics.html#ySquarePvalue(double, double)">ySquarePvalue</a></strong>(double N,
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double ysqr)</code>
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<div class="block">Returns the p-value of a Y-square statistic.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>static double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/Statistics.html#ySquareTest(int, double[], double[])">ySquareTest</a></strong>(int N,
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double[] measured,
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double[] expected)</code>
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<div class="block">Do a Y-square test on the given data.</div>
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</td>
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<h3>Methods inherited from class java.lang.<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></h3>
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<code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</a></code></li>
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<h4>chiSquareTest</h4>
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<pre>public static double chiSquareTest(double[] measured,
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double[] expected)</pre>
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<div class="block">Do a chi-square test on the given data. The null hypothesis is that the
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data was drawn from the distribution given by <TT>expected</TT>. The
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<TT>measured</TT> and <TT>expected</TT> arrays must be the same length.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>measured</code> - Measured count in each bin.</dd><dd><code>expected</code> - Expected count in each bin.</dd>
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<dt><span class="strong">Returns:</span></dt><dd>Chi-square statistic.</dd></dl>
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</li>
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</ul>
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<h4>chiSquarePvalue</h4>
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<pre>public static double chiSquarePvalue(double N,
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double chisqr)</pre>
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<div class="block">Returns the p-value of a chi-square statistic.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>N</code> - Degrees of freedom.</dd><dd><code>chisqr</code> - Chi-square statistic.</dd>
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<dt><span class="strong">Returns:</span></dt><dd>P-value.</dd></dl>
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</li>
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</ul>
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<a name="bernoulliChiSquareTest(long, long)">
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<h4>bernoulliChiSquareTest</h4>
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<pre>public static double bernoulliChiSquareTest(long total,
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long measured)</pre>
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<div class="block">Do a Bernoulli chi-square test on the given data. The null hypothesis is
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that the data was drawn from a Bernoulli distribution with both outcomes
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equally likely (e.g., a fair coin). <TT>total</TT> is the total number of
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trials. <TT>measured</TT> is the number of trials yielding one of the
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outcomes. (<TT>total</TT> − <TT>measured</TT>) is the
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number of trials yielding the other outcome.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>total</code> - Total number of trials.</dd><dd><code>measured</code> - Number of trials yielding one of the outcomes.</dd>
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<dt><span class="strong">Returns:</span></dt><dd>Chi-square statistic.</dd></dl>
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<h4>bernoulliChiSquarePvalue</h4>
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<pre>public static double bernoulliChiSquarePvalue(double chisqr)</pre>
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<div class="block">Returns the p-value of a Bernoulli chi-square statistic.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>chisqr</code> - Chi-square statistic.</dd>
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<dt><span class="strong">Returns:</span></dt><dd>P-value.</dd></dl>
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</li>
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</ul>
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<a name="ySquareTest(int, double[], double[])">
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<h4>ySquareTest</h4>
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<pre>public static double ySquareTest(int N,
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double[] measured,
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double[] expected)</pre>
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<div class="block">Do a Y-square test on the given data. The null hypothesis is that the
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data was drawn from the distribution given by <TT>expected</TT>. The
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<TT>measured</TT> and <TT>expected</TT> arrays must be the same length.
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<P>
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The Y-square test is similar to the chi-square test, except the Y-square
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statistic is valid even if the expected counts in some of the bins are
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small, which is not true of the chi-square statistic. For further
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information, see:
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<P>
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L. Lucy. Hypothesis testing for meagre data sets. <I>Monthly Notices of
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the Royal Astronomical Society,</I> 318(1):92-100, October 2000.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>N</code> - Degrees of freedom.</dd><dd><code>measured</code> - Measured count in each bin.</dd><dd><code>expected</code> - Expected count in each bin.</dd>
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<dt><span class="strong">Returns:</span></dt><dd>Y-square statistic.</dd></dl>
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</li>
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</ul>
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<a name="ySquarePvalue(double, double)">
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<h4>ySquarePvalue</h4>
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<pre>public static double ySquarePvalue(double N,
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double ysqr)</pre>
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<div class="block">Returns the p-value of a Y-square statistic.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>N</code> - Degrees of freedom.</dd><dd><code>ysqr</code> - Y-square statistic.</dd>
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<dt><span class="strong">Returns:</span></dt><dd>P-value.</dd></dl>
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</li>
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</ul>
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<a name="ksTest(double[])">
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<h4>ksTest</h4>
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<pre>public static double ksTest(double[] data)</pre>
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<div class="block">Do a Kolmogorov-Smirnov (K-S) test on the given data. The null hypothesis
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is that the data was drawn from a uniform distribution between 0.0 and
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1.0.
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<P>
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The values in the <TT>data</TT> array must all be in the range 0.0
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through 1.0 and must be in ascending numerical order. The
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<TT>ksTest()</TT> method does not sort the data itself because the
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process that produced the data might already have sorted the data. If
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necessary, call <a href="../../../edu/rit/util/Sorting.html#sort(double[])"><code>Sorting.sort</code></a><TT>(data)</TT> before calling <TT>ksTest(data)</TT>.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>data</code> - Data array.</dd>
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<dt><span class="strong">Returns:</span></dt><dd>K-S statistic.</dd></dl>
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</li>
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<a name="ksTest(double[], edu.rit.numeric.Function)">
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<h4>ksTest</h4>
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<pre>public static double ksTest(double[] data,
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<a href="../../../edu/rit/numeric/Function.html" title="interface in edu.rit.numeric">Function</a> cdf)</pre>
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<div class="block">Do a Kolmogorov-Smirnov (K-S) test on the given data. The null hypothesis
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is that the data was drawn from the distribution specified by the given
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<a href="../../../edu/rit/numeric/Function.html" title="interface in edu.rit.numeric">Function</a>. <TT>cdf.f(x)</TT> must return the value of the
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cumulative distribution function at <I>x</I>, in the range 0.0 through
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1.0.
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<P>
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The values in the <TT>data</TT> array must all be in the domain of
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<TT>cdf</TT> and must be in ascending numerical order. The
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<TT>ksTest()</TT> method does not sort the data itself because the
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process that produced the data might already have sorted the data. If
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necessary, call <a href="../../../edu/rit/util/Sorting.html#sort(double[])"><code>Sorting.sort</code></a><TT>(data)</TT> before calling <TT>ksTest(data)</TT>.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>data</code> - Data array.</dd><dd><code>cdf</code> - Cumulative distribution function.</dd>
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<dt><span class="strong">Returns:</span></dt><dd>K-S statistic.</dd></dl>
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<h4>ksPvalue</h4>
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<pre>public static double ksPvalue(double N,
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double D)</pre>
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<div class="block">Returns the p-value of a K-S statistic.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>N</code> - Number of data points.</dd><dd><code>D</code> - K-S statistic.</dd>
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<dt><span class="strong">Returns:</span></dt><dd>P-value.</dd></dl>
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<h4>normalPvalue</h4>
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<pre>public static double normalPvalue(double x,
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double mean,
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double stddev)</pre>
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<div class="block">Returns the p-value of a statistic drawn from a normal distribution.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - Statistic.</dd><dd><code>mean</code> - Mean of the normal distribution.</dd><dd><code>stddev</code> - Standard deviation of the normal distribution.</dd>
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<dt><span class="strong">Returns:</span></dt><dd>P-value.</dd></dl>
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<a name="tTestUnequalVariance(edu.rit.numeric.Series, edu.rit.numeric.Series)">
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<h4>tTestUnequalVariance</h4>
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<pre>public static double[] tTestUnequalVariance(<a href="../../../edu/rit/numeric/Series.html" title="class in edu.rit.numeric">Series</a> data1,
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<a href="../../../edu/rit/numeric/Series.html" title="class in edu.rit.numeric">Series</a> data2)</pre>
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<div class="block">Do an unequal-variance <I>t</I>-test on the two given data series. The
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null hypothesis is that the two data series have the same mean; however,
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the two series are assumed to have different variances. An array of two
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doubles is returned; element 0 gives the <I>t</I> statistic; element 1
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gives the <I>p</I>-value (significance) of the <I>t</I> statistic.
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Roughly speaking, the <I>p</I>-value is the probability that the
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hypothesis is true. If the <I>p</I>-value falls below a significance
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threshold, the hypothesis is not true, and the two data series have
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different means.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>data1</code> - First data series.</dd><dd><code>data2</code> - Second data series.</dd>
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<dt><span class="strong">Returns:</span></dt><dd><I>t</I> statistic and its <I>p</I>-value.</dd></dl>
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<p class="legalCopy"><small><FONT SIZE="-2">Copyright © 2013–2016 by Alan Kaminsky. All rights reserved. Send comments to ark</FONT><FONT SIZE="1" COLOR="#FFFFFF">­</FONT><FONT SIZE="-2">@</FONT><FONT SIZE="1" COLOR="#FFFFFF">­</FONT><FONT SIZE="-2">cs.rit.edu.</FONT></small></p>
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