Added two-sample (binned comparison) ChiSquare test
JIRA: MATH-160 Thanks to: Matthias Hummel git-svn-id: https://svn.apache.org/repos/asf/jakarta/commons/proper/math/trunk@550285 13f79535-47bb-0310-9956-ffa450edef68
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Phil Steitz
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@ -211,4 +211,118 @@ public interface ChiSquareTest {
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*/
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boolean chiSquareTest(long[][] counts, double alpha)
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throws IllegalArgumentException, MathException;
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/**
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* <p>Computes a
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* <a href="http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/chi2samp.htm">
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* Chi-Square two sample test statistic</a> comparing bin frequency counts
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* in <code>observed1</code> and <code>observed2</code>. The
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* sums of frequency counts in the two samples are not required to be the
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* same. The formula used to compute the test statistic is</p>
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* <code>
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* ∑[(K * observed1[i] - observed2[i]/K)<sup>2</sup> / (observed1[i] + observed2[i])]
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* </code> where
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* <br/><code>K = &sqrt;[&sum(observed2 / ∑(observed1)]</code>
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* </p>
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* <p>This statistic can be used to perform a Chi-Square test evaluating the null hypothesis that
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* both observed counts follow the same distribution.
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* <p>
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* <strong>Preconditions</strong>: <ul>
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* <li>Observed counts must be non-negative.
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* </li>
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* <li>Observed counts for a specific bin must not both be zero.
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* </li>
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* <li>Observed counts for a specific sample must not all be 0.
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* </li>
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* <li>The arrays <code>observed1</code> and <code>observed2</code> must have the same length and
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* their common length must be at least 2.
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* </li></ul><p>
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* If any of the preconditions are not met, an
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* <code>IllegalArgumentException</code> is thrown.
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*
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* @param observed1 array of observed frequency counts of the first data set
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* @param observed2 array of observed frequency counts of the second data set
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* @return chiSquare statistic
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* @throws IllegalArgumentException if preconditions are not met
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*/
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double chiSquareDataSetsComparison(long[] observed1, long[] observed2)
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throws IllegalArgumentException;
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/**
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* <p>Returns the <i>observed significance level</i>, or <a href=
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* "http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#pvalue">
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* p-value</a>, associated with a Chi-Square two sample test comparing
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* bin frequency counts in <code>observed1</code> and
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* <code>observed2</code>.
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* </p>
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* <p>The number returned is the smallest significance level at which one
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* can reject the null hypothesis that the observed counts conform to the
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* same distribution.
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* </p>
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* <p>See {@link #chiSquareDataSetsComparison(long[], long[]) for details
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* on the formula used to compute the test statistic. The degrees of
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* of freedom used to perform the test is one less than the common length
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* of the input observed count arrays.
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* </p>
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* <strong>Preconditions</strong>: <ul>
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* <li>Observed counts must be non-negative.
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* </li>
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* <li>Observed counts for a specific bin must not both be zero.
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* </li>
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* <li>Observed counts for a specific sample must not all be 0.
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* </li>
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* <li>The arrays <code>observed1</code> and <code>observed2</code> must
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* have the same length and
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* their common length must be at least 2.
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* </li></ul><p>
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* If any of the preconditions are not met, an
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* <code>IllegalArgumentException</code> is thrown.
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*
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* @param observed1 array of observed frequency counts of the first data set
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* @param observed2 array of observed frequency counts of the second data set
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* @return p-value
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* @throws IllegalArgumentException if preconditions are not met
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* @throws MathException if an error occurs computing the p-value
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*/
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double chiSquareTestDataSetsComparison(long[] observed1, long[] observed2)
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throws IllegalArgumentException, MathException;
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/**
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* <p>Performs a Chi-Square two sample test comparing two binned data
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* sets. The test evaluates the null hypothesis that the two lists of
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* observed counts conform to the same frequency distribution, with
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* significance level <code>alpha</code>. Returns true iff the null
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* hypothesis can be rejected with 100 * (1 - alpha) percent confidence.
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* </p>
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* <p>See {@link #chiSquareDataSetsComparison(double[], double[])} for
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* details on the forumla used to compute the Chisquare statistic used
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* in the test. The degrees of of freedom used to perform the test is
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* one less than the common length of the input observed count arrays.
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* </p>
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* <strong>Preconditions</strong>: <ul>
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* <li>Observed counts must be non-negative.
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* </li>
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* <li>Observed counts for a specific bin must not both be zero.
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* </li>
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* <li>Observed counts for a specific sample must not all be 0.
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* </li>
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* <li>The arrays <code>observed1</code> and <code>observed2</code> must
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* have the same length and their common length must be at least 2.
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* </li>
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* <li> <code> 0 < alpha < 0.5 </code>
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* </li></ul><p>
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* If any of the preconditions are not met, an
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* <code>IllegalArgumentException</code> is thrown.
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*
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* @param observed1 array of observed frequency counts of the first data set
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* @param observed2 array of observed frequency counts of the second data set
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* @param alpha significance level of the test
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* @return true iff null hypothesis can be rejected with confidence
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* 1 - alpha
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* @throws IllegalArgumentException if preconditions are not met
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* @throws MathException if an error occurs performing the test
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*/
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boolean chiSquareTestDataSetsComparison(long[] observed1, long[] observed2, double alpha)
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throws IllegalArgumentException, MathException;
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}
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@ -172,6 +172,99 @@ public class ChiSquareTestImpl implements ChiSquareTest {
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return (chiSquareTest(counts) < alpha);
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}
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/**
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* @param observed1 array of observed frequency counts of the first data set
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* @param observed2 array of observed frequency counts of the second data set
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* @return chi-square test statistic
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* @throws IllegalArgumentException if preconditions are not met
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*/
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public double chiSquareDataSetsComparison(long[] observed1, long[] observed2)
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throws IllegalArgumentException {
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// Make sure lengths are same
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if ((observed1.length < 2) || (observed1.length != observed2.length)) {
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throw new IllegalArgumentException(
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"oberved1, observed2 array lengths incorrect");
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}
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// Ensure non-negative counts
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if (!isNonNegative(observed1) || !isNonNegative(observed2)) {
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throw new IllegalArgumentException(
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"observed counts must be non-negative");
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}
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// Compute and compare count sums
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long countSum1 = 0;
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long countSum2 = 0;
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boolean unequalCounts = false;
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double weight = 0.0;
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for (int i = 0; i < observed1.length; i++) {
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countSum1 += observed1[i];
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countSum2 += observed2[i];
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}
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// Ensure neither sample is uniformly 0
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if (countSum1 * countSum2 == 0) {
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throw new IllegalArgumentException(
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"observed counts cannot all be 0");
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}
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// Compare and compute weight only if different
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unequalCounts = (countSum1 != countSum2);
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if (unequalCounts) {
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weight = Math.sqrt((double) countSum1 / (double) countSum2);
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}
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// Compute ChiSquare statistic
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double sumSq = 0.0d;
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double dev = 0.0d;
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double obs1 = 0.0d;
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double obs2 = 0.0d;
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for (int i = 0; i < observed1.length; i++) {
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if (observed1[i] == 0 && observed2[i] == 0) {
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throw new IllegalArgumentException(
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"observed counts must not both be zero");
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} else {
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obs1 = (double) observed1[i];
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obs2 = (double) observed2[i];
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if (unequalCounts) { // apply weights
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dev = obs1/weight - obs2 * weight;
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} else {
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dev = obs1 - obs2;
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}
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sumSq += (dev * dev) / (obs1 + obs2);
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}
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}
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return sumSq;
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}
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/**
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* @param observed1 array of observed frequency counts of the first data set
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* @param observed2 array of observed frequency counts of the second data set
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* @return p-value
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* @throws IllegalArgumentException if preconditions are not met
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* @throws MathException if an error occurs computing the p-value
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*/
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public double chiSquareTestDataSetsComparison(long[] observed1, long[] observed2)
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throws IllegalArgumentException, MathException {
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distribution.setDegreesOfFreedom((double) observed1.length - 1);
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return 1 - distribution.cumulativeProbability(
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chiSquareDataSetsComparison(observed1, observed2));
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}
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/**
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* @param observed1 array of observed frequency counts of the first data set
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* @param observed2 array of observed frequency counts of the second data set
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* @param alpha significance level of the test
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* @return true iff null hypothesis can be rejected with confidence
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* 1 - alpha
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* @throws IllegalArgumentException if preconditions are not met
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* @throws MathException if an error occurs performing the test
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*/
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public boolean chiSquareTestDataSetsComparison(long[] observed1, long[] observed2,
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double alpha) throws IllegalArgumentException, MathException {
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if ((alpha <= 0) || (alpha > 0.5)) {
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throw new IllegalArgumentException(
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"bad significance level: " + alpha);
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}
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return (chiSquareTestDataSetsComparison(observed1, observed2) < alpha);
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}
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/**
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* Checks to make sure that the input long[][] array is rectangular,
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* has at least 2 rows and 2 columns, and has all non-negative entries,
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@ -281,10 +374,12 @@ public class ChiSquareTestImpl implements ChiSquareTest {
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}
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return true;
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}
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/**
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* Modify the distribution used to compute inference statistics.
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* @param value the new distribution
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*
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* @param value
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* the new distribution
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* @since 1.2
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*/
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public void setDistribution(ChiSquaredDistribution value) {
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@ -276,4 +276,31 @@ public class TestUtils {
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return chiSquareTest. chiSquareTest(counts);
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}
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/**
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* @see org.apache.commons.math.stat.inference.ChiSquareTest#chiSquareDataSetsComparison(double[], double[])
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*/
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public static double chiSquareDataSetsComparison(long[] observed1, long[] observed2)
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throws IllegalArgumentException {
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return chiSquareTest.chiSquareDataSetsComparison(observed1, observed2);
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}
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/**
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* @see org.apache.commons.math.stat.inference.ChiSquareTest#chiSquareTestDataSetsComparison(double[], double[])
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*/
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public static double chiSquareTestDataSetsComparison(long[] observed1, long[] observed2)
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throws IllegalArgumentException, MathException {
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return chiSquareTest.chiSquareTestDataSetsComparison(observed1, observed2);
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}
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/**
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* @see org.apache.commons.math.stat.inference.ChiSquareTest#chiSquareTestDataSetsComparison(double[], double[], double)
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*/
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public static boolean chiSquareTestDataSetsComparison(long[] observed1, long[] observed2,
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double alpha)
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throws IllegalArgumentException, MathException {
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return chiSquareTest.chiSquareTestDataSetsComparison(observed1, observed2, alpha);
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}
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}
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@ -193,4 +193,70 @@ public class ChiSquareTestTest extends TestCase {
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assertEquals("chi-square p-value", 0.0462835770603,
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testStatistic.chiSquareTest(counts), 1E-9);
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}
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/** Target values verified using DATAPLOT version 2006.3 */
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public void testChiSquareDataSetsComparisonEqualCounts()
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throws Exception {
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long[] observed1 = {10, 12, 12, 10};
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long[] observed2 = {5, 15, 14, 10};
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assertEquals("chi-square p value", 0.541096,
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testStatistic.chiSquareTestDataSetsComparison(
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observed1, observed2), 1E-6);
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assertEquals("chi-square test statistic", 2.153846,
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testStatistic.chiSquareDataSetsComparison(
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observed1, observed2), 1E-6);
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assertFalse("chi-square test result",
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testStatistic.chiSquareTestDataSetsComparison(
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observed1, observed2, 0.4));
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}
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/** Target values verified using DATAPLOT version 2006.3 */
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public void testChiSquareDataSetsComparisonUnEqualCounts()
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throws Exception {
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long[] observed1 = {10, 12, 12, 10, 15};
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long[] observed2 = {15, 10, 10, 15, 5};
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assertEquals("chi-square p value", 0.124115,
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testStatistic.chiSquareTestDataSetsComparison(
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observed1, observed2), 1E-6);
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assertEquals("chi-square test statistic", 7.232189,
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testStatistic.chiSquareDataSetsComparison(
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observed1, observed2), 1E-6);
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assertTrue("chi-square test result",
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testStatistic.chiSquareTestDataSetsComparison(
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observed1, observed2, 0.13));
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assertFalse("chi-square test result",
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testStatistic.chiSquareTestDataSetsComparison(
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observed1, observed2, 0.12));
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}
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public void testChiSquareDataSetsComparisonBadCounts()
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throws Exception {
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long[] observed1 = {10, -1, 12, 10, 15};
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long[] observed2 = {15, 10, 10, 15, 5};
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try {
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testStatistic.chiSquareTestDataSetsComparison(
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observed1, observed2);
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fail("Expecting IllegalArgumentException - negative count");
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} catch (IllegalArgumentException ex) {
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// expected
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}
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long[] observed3 = {10, 0, 12, 10, 15};
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long[] observed4 = {15, 0, 10, 15, 5};
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try {
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testStatistic.chiSquareTestDataSetsComparison(
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observed3, observed4);
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fail("Expecting IllegalArgumentException - double 0's");
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} catch (IllegalArgumentException ex) {
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// expected
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}
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long[] observed5 = {10, 10, 12, 10, 15};
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long[] observed6 = {0, 0, 0, 0, 0};
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try {
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testStatistic.chiSquareTestDataSetsComparison(
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observed5, observed6);
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fail("Expecting IllegalArgumentException - vanishing counts");
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} catch (IllegalArgumentException ex) {
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// expected
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}
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}
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}
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@ -84,6 +84,9 @@ Commons Math Release Notes</title>
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<action dev="psteitz" type="update" issue="MATH-158" due-to "Hasan Diwan">
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Added log function to MathUtils.
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</action>
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<action dev="psteitz" type="update" issue="MATH-160" due-to "Matthias Hummel">
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Added two sample (binned comparison) ChiSquare test.
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</action>
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</release>
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<release version="1.1" date="2005-12-17"
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description="This is a maintenance release containing bug fixes and enhancements.
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