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From pste...@apache.org
Subject svn commit: r811685 [12/24] - in /commons/proper/math/trunk: ./ src/main/java/org/apache/commons/math/ src/main/java/org/apache/commons/math/analysis/ src/main/java/org/apache/commons/math/analysis/integration/ src/main/java/org/apache/commons/math/ana...
Date Sat, 05 Sep 2009 17:37:05 GMT
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/TTest.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/TTest.java?rev=811685&r1=811684&r2=811685&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/TTest.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/TTest.java Sat Sep  5 17:36:48 2009
@@ -38,19 +38,19 @@
  * Significance levels are always specified as numbers between 0 and 0.5
  * (e.g. tests at the 95% level  use <code>alpha=0.05</code>).</p>
  * <p>
- * Input to tests can be either <code>double[]</code> arrays or 
+ * Input to tests can be either <code>double[]</code> arrays or
  * {@link StatisticalSummary} instances.</p>
- * 
  *
- * @version $Revision$ $Date$ 
+ *
+ * @version $Revision$ $Date$
  */
 public interface TTest {
     /**
-     * Computes a paired, 2-sample t-statistic based on the data in the input 
+     * Computes a paired, 2-sample t-statistic based on the data in the input
      * arrays.  The t-statistic returned is equivalent to what would be returned by
      * computing the one-sample t-statistic {@link #t(double, double[])}, with
-     * <code>mu = 0</code> and the sample array consisting of the (signed) 
-     * differences between corresponding entries in <code>sample1</code> and 
+     * <code>mu = 0</code> and the sample array consisting of the (signed)
+     * differences between corresponding entries in <code>sample1</code> and
      * <code>sample2.</code>
      * <p>
      * <strong>Preconditions</strong>: <ul>
@@ -68,24 +68,24 @@
     public abstract double pairedT(double[] sample1, double[] sample2)
         throws IllegalArgumentException, MathException;
     /**
-     * Returns the <i>observed significance level</i>, or 
-     * <i> p-value</i>, associated with a paired, two-sample, two-tailed t-test 
+     * Returns the <i>observed significance level</i>, or
+     * <i> p-value</i>, associated with a paired, two-sample, two-tailed t-test
      * based on the data in the input arrays.
      * <p>
      * The number returned is the smallest significance level
      * at which one can reject the null hypothesis that the mean of the paired
-     * differences is 0 in favor of the two-sided alternative that the mean paired 
-     * difference is not equal to 0. For a one-sided test, divide the returned 
+     * differences is 0 in favor of the two-sided alternative that the mean paired
+     * difference is not equal to 0. For a one-sided test, divide the returned
      * value by 2.</p>
      * <p>
      * This test is equivalent to a one-sample t-test computed using
      * {@link #tTest(double, double[])} with <code>mu = 0</code> and the sample
-     * array consisting of the signed differences between corresponding elements of 
+     * array consisting of the signed differences between corresponding elements of
      * <code>sample1</code> and <code>sample2.</code></p>
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the p-value depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
      * here</a></p>
      * <p>
@@ -103,24 +103,24 @@
     public abstract double pairedTTest(double[] sample1, double[] sample2)
         throws IllegalArgumentException, MathException;
     /**
-     * Performs a paired t-test evaluating the null hypothesis that the 
+     * Performs a paired t-test evaluating the null hypothesis that the
      * mean of the paired differences between <code>sample1</code> and
-     * <code>sample2</code> is 0 in favor of the two-sided alternative that the 
-     * mean paired difference is not equal to 0, with significance level 
+     * <code>sample2</code> is 0 in favor of the two-sided alternative that the
+     * mean paired difference is not equal to 0, with significance level
      * <code>alpha</code>.
      * <p>
-     * Returns <code>true</code> iff the null hypothesis can be rejected with 
-     * confidence <code>1 - alpha</code>.  To perform a 1-sided test, use 
+     * Returns <code>true</code> iff the null hypothesis can be rejected with
+     * confidence <code>1 - alpha</code>.  To perform a 1-sided test, use
      * <code>alpha * 2</code></p>
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the test depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
      * here</a></p>
      * <p>
      * <strong>Preconditions</strong>: <ul>
-     * <li>The input array lengths must be the same and their common length 
+     * <li>The input array lengths must be the same and their common length
      * must be at least 2.
      * </li>
      * <li> <code> 0 < alpha < 0.5 </code>
@@ -129,7 +129,7 @@
      * @param sample1 array of sample data values
      * @param sample2 array of sample data values
      * @param alpha significance level of the test
-     * @return true if the null hypothesis can be rejected with 
+     * @return true if the null hypothesis can be rejected with
      * confidence 1 - alpha
      * @throws IllegalArgumentException if the preconditions are not met
      * @throws MathException if an error occurs performing the test
@@ -140,7 +140,7 @@
         double alpha)
         throws IllegalArgumentException, MathException;
     /**
-     * Computes a <a href="http://www.itl.nist.gov/div898/handbook/prc/section2/prc22.htm#formula"> 
+     * Computes a <a href="http://www.itl.nist.gov/div898/handbook/prc/section2/prc22.htm#formula">
      * t statistic </a> given observed values and a comparison constant.
      * <p>
      * This statistic can be used to perform a one sample t-test for the mean.
@@ -158,7 +158,7 @@
         throws IllegalArgumentException;
     /**
      * Computes a <a href="http://www.itl.nist.gov/div898/handbook/prc/section2/prc22.htm#formula">
-     * t statistic </a> to use in comparing the mean of the dataset described by 
+     * t statistic </a> to use in comparing the mean of the dataset described by
      * <code>sampleStats</code> to <code>mu</code>.
      * <p>
      * This statistic can be used to perform a one sample t-test for the mean.
@@ -175,7 +175,7 @@
     public abstract double t(double mu, StatisticalSummary sampleStats)
         throws IllegalArgumentException;
     /**
-     * Computes a 2-sample t statistic,  under the hypothesis of equal 
+     * Computes a 2-sample t statistic,  under the hypothesis of equal
      * subpopulation variances.  To compute a t-statistic without the
      * equal variances hypothesis, use {@link #t(double[], double[])}.
      * <p>
@@ -186,15 +186,15 @@
      * <p>
      * &nbsp;&nbsp;<code>  t = (m1 - m2) / (sqrt(1/n1 +1/n2) sqrt(var))</code>
      * </p><p>
-     * where <strong><code>n1</code></strong> is the size of first sample; 
-     * <strong><code> n2</code></strong> is the size of second sample; 
-     * <strong><code> m1</code></strong> is the mean of first sample;  
+     * where <strong><code>n1</code></strong> is the size of first sample;
+     * <strong><code> n2</code></strong> is the size of second sample;
+     * <strong><code> m1</code></strong> is the mean of first sample;
      * <strong><code> m2</code></strong> is the mean of second sample</li>
      * </ul>
      * and <strong><code>var</code></strong> is the pooled variance estimate:
      * </p><p>
      * <code>var = sqrt(((n1 - 1)var1 + (n2 - 1)var2) / ((n1-1) + (n2-1)))</code>
-     * </p><p> 
+     * </p><p>
      * with <strong><code>var1<code></strong> the variance of the first sample and
      * <strong><code>var2</code></strong> the variance of the second sample.
      * </p><p>
@@ -222,11 +222,11 @@
      * &nbsp;&nbsp; <code>  t = (m1 - m2) / sqrt(var1/n1 + var2/n2)</code>
      * </p><p>
      *  where <strong><code>n1</code></strong> is the size of the first sample
-     * <strong><code> n2</code></strong> is the size of the second sample; 
-     * <strong><code> m1</code></strong> is the mean of the first sample;  
+     * <strong><code> n2</code></strong> is the size of the second sample;
+     * <strong><code> m1</code></strong> is the mean of the first sample;
      * <strong><code> m2</code></strong> is the mean of the second sample;
      * <strong><code> var1</code></strong> is the variance of the first sample;
-     * <strong><code> var2</code></strong> is the variance of the second sample;  
+     * <strong><code> var2</code></strong> is the variance of the second sample;
      * </p><p>
      * <strong>Preconditions</strong>: <ul>
      * <li>The observed array lengths must both be at least 2.
@@ -242,7 +242,7 @@
     /**
      * Computes a 2-sample t statistic </a>, comparing the means of the datasets
      * described by two {@link StatisticalSummary} instances, without the
-     * assumption of equal subpopulation variances.  Use 
+     * assumption of equal subpopulation variances.  Use
      * {@link #homoscedasticT(StatisticalSummary, StatisticalSummary)} to
      * compute a t-statistic under the equal variances assumption.
      * <p>
@@ -253,11 +253,11 @@
      * <p>
      * &nbsp;&nbsp; <code>  t = (m1 - m2) / sqrt(var1/n1 + var2/n2)</code>
      * </p><p>
-     * where <strong><code>n1</code></strong> is the size of the first sample; 
-     * <strong><code> n2</code></strong> is the size of the second sample; 
-     * <strong><code> m1</code></strong> is the mean of the first sample;  
+     * where <strong><code>n1</code></strong> is the size of the first sample;
+     * <strong><code> n2</code></strong> is the size of the second sample;
+     * <strong><code> m1</code></strong> is the mean of the first sample;
      * <strong><code> m2</code></strong> is the mean of the second sample
-     * <strong><code> var1</code></strong> is the variance of the first sample;  
+     * <strong><code> var1</code></strong> is the variance of the first sample;
      * <strong><code> var2</code></strong> is the variance of the second sample
      * </p><p>
      * <strong>Preconditions</strong>: <ul>
@@ -278,7 +278,7 @@
      * Computes a 2-sample t statistic, comparing the means of the datasets
      * described by two {@link StatisticalSummary} instances, under the
      * assumption of equal subpopulation variances.  To compute a t-statistic
-     * without the equal variances assumption, use 
+     * without the equal variances assumption, use
      * {@link #t(StatisticalSummary, StatisticalSummary)}.
      * <p>
      * This statistic can be used to perform a (homoscedastic) two-sample
@@ -288,14 +288,14 @@
      * <p>
      * &nbsp;&nbsp;<code>  t = (m1 - m2) / (sqrt(1/n1 +1/n2) sqrt(var))</code>
      * </p><p>
-     * where <strong><code>n1</code></strong> is the size of first sample; 
-     * <strong><code> n2</code></strong> is the size of second sample; 
-     * <strong><code> m1</code></strong> is the mean of first sample;  
+     * where <strong><code>n1</code></strong> is the size of first sample;
+     * <strong><code> n2</code></strong> is the size of second sample;
+     * <strong><code> m1</code></strong> is the mean of first sample;
      * <strong><code> m2</code></strong> is the mean of second sample
      * and <strong><code>var</code></strong> is the pooled variance estimate:
      * </p><p>
      * <code>var = sqrt(((n1 - 1)var1 + (n2 - 1)var2) / ((n1-1) + (n2-1)))</code>
-     * </p><p> 
+     * </p><p>
      * with <strong><code>var1<code></strong> the variance of the first sample and
      * <strong><code>var2</code></strong> the variance of the second sample.
      * </p><p>
@@ -314,19 +314,19 @@
         StatisticalSummary sampleStats2)
         throws IllegalArgumentException;
     /**
-     * Returns the <i>observed significance level</i>, or 
-     * <i>p-value</i>, associated with a one-sample, two-tailed t-test 
+     * Returns the <i>observed significance level</i>, or
+     * <i>p-value</i>, associated with a one-sample, two-tailed t-test
      * comparing the mean of the input array with the constant <code>mu</code>.
      * <p>
      * The number returned is the smallest significance level
-     * at which one can reject the null hypothesis that the mean equals 
+     * at which one can reject the null hypothesis that the mean equals
      * <code>mu</code> in favor of the two-sided alternative that the mean
-     * is different from <code>mu</code>. For a one-sided test, divide the 
+     * is different from <code>mu</code>. For a one-sided test, divide the
      * returned value by 2.</p>
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the test depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">here</a>
      * </p><p>
      * <strong>Preconditions</strong>: <ul>
@@ -346,8 +346,8 @@
      * two-sided t-test</a> evaluating the null hypothesis that the mean of the population from
      * which <code>sample</code> is drawn equals <code>mu</code>.
      * <p>
-     * Returns <code>true</code> iff the null hypothesis can be 
-     * rejected with confidence <code>1 - alpha</code>.  To 
+     * Returns <code>true</code> iff the null hypothesis can be
+     * rejected with confidence <code>1 - alpha</code>.  To
      * perform a 1-sided test, use <code>alpha * 2</code></p>
      * <p>
      * <strong>Examples:</strong><br><ol>
@@ -355,14 +355,14 @@
      * the 95% level, use <br><code>tTest(mu, sample, 0.05) </code>
      * </li>
      * <li>To test the (one-sided) hypothesis <code> sample mean < mu </code>
-     * at the 99% level, first verify that the measured sample mean is less 
-     * than <code>mu</code> and then use 
+     * at the 99% level, first verify that the measured sample mean is less
+     * than <code>mu</code> and then use
      * <br><code>tTest(mu, sample, 0.02) </code>
      * </li></ol></p>
      * <p>
      * <strong>Usage Note:</strong><br>
-     * The validity of the test depends on the assumptions of the one-sample 
-     * parametric t-test procedure, as discussed 
+     * The validity of the test depends on the assumptions of the one-sample
+     * parametric t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/sg_glos.html#one-sample">here</a>
      * </p><p>
      * <strong>Preconditions</strong>: <ul>
@@ -379,20 +379,20 @@
     public abstract boolean tTest(double mu, double[] sample, double alpha)
         throws IllegalArgumentException, MathException;
     /**
-     * Returns the <i>observed significance level</i>, or 
-     * <i>p-value</i>, associated with a one-sample, two-tailed t-test 
+     * Returns the <i>observed significance level</i>, or
+     * <i>p-value</i>, associated with a one-sample, two-tailed t-test
      * comparing the mean of the dataset described by <code>sampleStats</code>
      * with the constant <code>mu</code>.
      * <p>
      * The number returned is the smallest significance level
-     * at which one can reject the null hypothesis that the mean equals 
+     * at which one can reject the null hypothesis that the mean equals
      * <code>mu</code> in favor of the two-sided alternative that the mean
-     * is different from <code>mu</code>. For a one-sided test, divide the 
+     * is different from <code>mu</code>. For a one-sided test, divide the
      * returned value by 2.</p>
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the test depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
      * here</a></p>
      * <p>
@@ -423,14 +423,14 @@
      * the 95% level, use <br><code>tTest(mu, sampleStats, 0.05) </code>
      * </li>
      * <li>To test the (one-sided) hypothesis <code> sample mean < mu </code>
-     * at the 99% level, first verify that the measured sample mean is less 
-     * than <code>mu</code> and then use 
+     * at the 99% level, first verify that the measured sample mean is less
+     * than <code>mu</code> and then use
      * <br><code>tTest(mu, sampleStats, 0.02) </code>
      * </li></ol></p>
      * <p>
      * <strong>Usage Note:</strong><br>
-     * The validity of the test depends on the assumptions of the one-sample 
-     * parametric t-test procedure, as discussed 
+     * The validity of the test depends on the assumptions of the one-sample
+     * parametric t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/sg_glos.html#one-sample">here</a>
      * </p><p>
      * <strong>Preconditions</strong>: <ul>
@@ -450,28 +450,28 @@
         double alpha)
         throws IllegalArgumentException, MathException;
     /**
-     * Returns the <i>observed significance level</i>, or 
-     * <i>p-value</i>, associated with a two-sample, two-tailed t-test 
+     * Returns the <i>observed significance level</i>, or
+     * <i>p-value</i>, associated with a two-sample, two-tailed t-test
      * comparing the means of the input arrays.
      * <p>
      * The number returned is the smallest significance level
      * at which one can reject the null hypothesis that the two means are
-     * equal in favor of the two-sided alternative that they are different. 
+     * equal in favor of the two-sided alternative that they are different.
      * For a one-sided test, divide the returned value by 2.</p>
      * <p>
      * The test does not assume that the underlying popuation variances are
-     * equal  and it uses approximated degrees of freedom computed from the 
+     * equal  and it uses approximated degrees of freedom computed from the
      * sample data to compute the p-value.  The t-statistic used is as defined in
      * {@link #t(double[], double[])} and the Welch-Satterthwaite approximation
-     * to the degrees of freedom is used, 
-     * as described 
+     * to the degrees of freedom is used,
+     * as described
      * <a href="http://www.itl.nist.gov/div898/handbook/prc/section3/prc31.htm">
      * here.</a>  To perform the test under the assumption of equal subpopulation
      * variances, use {@link #homoscedasticTTest(double[], double[])}.</p>
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the p-value depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
      * here</a></p>
      * <p>
@@ -488,8 +488,8 @@
     public abstract double tTest(double[] sample1, double[] sample2)
         throws IllegalArgumentException, MathException;
     /**
-     * Returns the <i>observed significance level</i>, or 
-     * <i>p-value</i>, associated with a two-sample, two-tailed t-test 
+     * Returns the <i>observed significance level</i>, or
+     * <i>p-value</i>, associated with a two-sample, two-tailed t-test
      * comparing the means of the input arrays, under the assumption that
      * the two samples are drawn from subpopulations with equal variances.
      * To perform the test without the equal variances assumption, use
@@ -497,7 +497,7 @@
      * <p>
      * The number returned is the smallest significance level
      * at which one can reject the null hypothesis that the two means are
-     * equal in favor of the two-sided alternative that they are different. 
+     * equal in favor of the two-sided alternative that they are different.
      * For a one-sided test, divide the returned value by 2.</p>
      * <p>
      * A pooled variance estimate is used to compute the t-statistic.  See
@@ -506,7 +506,7 @@
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the p-value depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
      * here</a></p>
      * <p>
@@ -525,17 +525,17 @@
         double[] sample2)
         throws IllegalArgumentException, MathException;
     /**
-     * Performs a 
+     * Performs a
      * <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm">
-     * two-sided t-test</a> evaluating the null hypothesis that <code>sample1</code> 
-     * and <code>sample2</code> are drawn from populations with the same mean, 
+     * two-sided t-test</a> evaluating the null hypothesis that <code>sample1</code>
+     * and <code>sample2</code> are drawn from populations with the same mean,
      * with significance level <code>alpha</code>.  This test does not assume
      * that the subpopulation variances are equal.  To perform the test assuming
-     * equal variances, use 
+     * equal variances, use
      * {@link #homoscedasticTTest(double[], double[], double)}.
      * <p>
      * Returns <code>true</code> iff the null hypothesis that the means are
-     * equal can be rejected with confidence <code>1 - alpha</code>.  To 
+     * equal can be rejected with confidence <code>1 - alpha</code>.  To
      * perform a 1-sided test, use <code>alpha * 2</code></p>
      * <p>
      * See {@link #t(double[], double[])} for the formula used to compute the
@@ -545,18 +545,18 @@
      * <p>
      * <strong>Examples:</strong><br><ol>
      * <li>To test the (2-sided) hypothesis <code>mean 1 = mean 2 </code> at
-     * the 95% level,  use 
+     * the 95% level,  use
      * <br><code>tTest(sample1, sample2, 0.05). </code>
      * </li>
      * <li>To test the (one-sided) hypothesis <code> mean 1 < mean 2 </code>,
      * at the 99% level, first verify that the measured  mean of <code>sample 1</code>
-     * is less than the mean of <code>sample 2</code> and then use 
+     * is less than the mean of <code>sample 2</code> and then use
      * <br><code>tTest(sample1, sample2, 0.02) </code>
      * </li></ol></p>
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the test depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
      * here</a></p>
      * <p>
@@ -569,7 +569,7 @@
      * @param sample1 array of sample data values
      * @param sample2 array of sample data values
      * @param alpha significance level of the test
-     * @return true if the null hypothesis can be rejected with 
+     * @return true if the null hypothesis can be rejected with
      * confidence 1 - alpha
      * @throws IllegalArgumentException if the preconditions are not met
      * @throws MathException if an error occurs performing the test
@@ -580,19 +580,19 @@
         double alpha)
         throws IllegalArgumentException, MathException;
     /**
-     * Performs a 
+     * Performs a
      * <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm">
-     * two-sided t-test</a> evaluating the null hypothesis that <code>sample1</code> 
-     * and <code>sample2</code> are drawn from populations with the same mean, 
+     * two-sided t-test</a> evaluating the null hypothesis that <code>sample1</code>
+     * and <code>sample2</code> are drawn from populations with the same mean,
      * with significance level <code>alpha</code>,  assuming that the
-     * subpopulation variances are equal.  Use 
+     * subpopulation variances are equal.  Use
      * {@link #tTest(double[], double[], double)} to perform the test without
      * the assumption of equal variances.
      * <p>
      * Returns <code>true</code> iff the null hypothesis that the means are
-     * equal can be rejected with confidence <code>1 - alpha</code>.  To 
+     * equal can be rejected with confidence <code>1 - alpha</code>.  To
      * perform a 1-sided test, use <code>alpha * 2.</code>  To perform the test
-     * without the assumption of equal subpopulation variances, use 
+     * without the assumption of equal subpopulation variances, use
      * {@link #tTest(double[], double[], double)}.</p>
      * <p>
      * A pooled variance estimate is used to compute the t-statistic. See
@@ -604,7 +604,7 @@
      * the 95% level, use <br><code>tTest(sample1, sample2, 0.05). </code>
      * </li>
      * <li>To test the (one-sided) hypothesis <code> mean 1 < mean 2, </code>
-     * at the 99% level, first verify that the measured mean of 
+     * at the 99% level, first verify that the measured mean of
      * <code>sample 1</code> is less than the mean of <code>sample 2</code>
      * and then use
      * <br><code>tTest(sample1, sample2, 0.02) </code>
@@ -612,7 +612,7 @@
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the test depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
      * here</a></p>
      * <p>
@@ -625,7 +625,7 @@
      * @param sample1 array of sample data values
      * @param sample2 array of sample data values
      * @param alpha significance level of the test
-     * @return true if the null hypothesis can be rejected with 
+     * @return true if the null hypothesis can be rejected with
      * confidence 1 - alpha
      * @throws IllegalArgumentException if the preconditions are not met
      * @throws MathException if an error occurs performing the test
@@ -636,25 +636,25 @@
         double alpha)
         throws IllegalArgumentException, MathException;
     /**
-     * Returns the <i>observed significance level</i>, or 
-     * <i>p-value</i>, associated with a two-sample, two-tailed t-test 
+     * Returns the <i>observed significance level</i>, or
+     * <i>p-value</i>, associated with a two-sample, two-tailed t-test
      * comparing the means of the datasets described by two StatisticalSummary
      * instances.
      * <p>
      * The number returned is the smallest significance level
      * at which one can reject the null hypothesis that the two means are
-     * equal in favor of the two-sided alternative that they are different. 
+     * equal in favor of the two-sided alternative that they are different.
      * For a one-sided test, divide the returned value by 2.</p>
      * <p>
      * The test does not assume that the underlying popuation variances are
-     * equal  and it uses approximated degrees of freedom computed from the 
+     * equal  and it uses approximated degrees of freedom computed from the
      * sample data to compute the p-value.   To perform the test assuming
-     * equal variances, use 
+     * equal variances, use
      * {@link #homoscedasticTTest(StatisticalSummary, StatisticalSummary)}.</p>
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the p-value depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
      * here</a></p>
      * <p>
@@ -674,8 +674,8 @@
         StatisticalSummary sampleStats2)
         throws IllegalArgumentException, MathException;
     /**
-     * Returns the <i>observed significance level</i>, or 
-     * <i>p-value</i>, associated with a two-sample, two-tailed t-test 
+     * Returns the <i>observed significance level</i>, or
+     * <i>p-value</i>, associated with a two-sample, two-tailed t-test
      * comparing the means of the datasets described by two StatisticalSummary
      * instances, under the hypothesis of equal subpopulation variances. To
      * perform a test without the equal variances assumption, use
@@ -683,7 +683,7 @@
      * <p>
      * The number returned is the smallest significance level
      * at which one can reject the null hypothesis that the two means are
-     * equal in favor of the two-sided alternative that they are different. 
+     * equal in favor of the two-sided alternative that they are different.
      * For a one-sided test, divide the returned value by 2.</p>
      * <p>
      * See {@link #homoscedasticT(double[], double[])} for the formula used to
@@ -692,7 +692,7 @@
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the p-value depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">here</a>
      * </p><p>
      * <strong>Preconditions</strong>: <ul>
@@ -711,9 +711,9 @@
         StatisticalSummary sampleStats2)
         throws IllegalArgumentException, MathException;
     /**
-     * Performs a 
+     * Performs a
      * <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm">
-     * two-sided t-test</a> evaluating the null hypothesis that 
+     * two-sided t-test</a> evaluating the null hypothesis that
      * <code>sampleStats1</code> and <code>sampleStats2</code> describe
      * datasets drawn from populations with the same mean, with significance
      * level <code>alpha</code>.   This test does not assume that the
@@ -722,7 +722,7 @@
      * {@link #homoscedasticTTest(StatisticalSummary, StatisticalSummary)}.
      * <p>
      * Returns <code>true</code> iff the null hypothesis that the means are
-     * equal can be rejected with confidence <code>1 - alpha</code>.  To 
+     * equal can be rejected with confidence <code>1 - alpha</code>.  To
      * perform a 1-sided test, use <code>alpha * 2</code></p>
      * <p>
      * See {@link #t(double[], double[])} for the formula used to compute the
@@ -732,19 +732,19 @@
      * <p>
      * <strong>Examples:</strong><br><ol>
      * <li>To test the (2-sided) hypothesis <code>mean 1 = mean 2 </code> at
-     * the 95%, use 
+     * the 95%, use
      * <br><code>tTest(sampleStats1, sampleStats2, 0.05) </code>
      * </li>
      * <li>To test the (one-sided) hypothesis <code> mean 1 < mean 2 </code>
-     * at the 99% level,  first verify that the measured mean of  
+     * at the 99% level,  first verify that the measured mean of
      * <code>sample 1</code> is less than  the mean of <code>sample 2</code>
-     * and then use 
+     * and then use
      * <br><code>tTest(sampleStats1, sampleStats2, 0.02) </code>
      * </li></ol></p>
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the test depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
      * here</a></p>
      * <p>
@@ -758,7 +758,7 @@
      * @param sampleStats1 StatisticalSummary describing sample data values
      * @param sampleStats2 StatisticalSummary describing sample data values
      * @param alpha significance level of the test
-     * @return true if the null hypothesis can be rejected with 
+     * @return true if the null hypothesis can be rejected with
      * confidence 1 - alpha
      * @throws IllegalArgumentException if the preconditions are not met
      * @throws MathException if an error occurs performing the test
@@ -768,4 +768,4 @@
         StatisticalSummary sampleStats2,
         double alpha)
         throws IllegalArgumentException, MathException;
-}
\ No newline at end of file
+}

Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/TTestImpl.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/TTestImpl.java?rev=811685&r1=811684&r2=811685&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/TTestImpl.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/TTestImpl.java Sat Sep  5 17:36:48 2009
@@ -35,14 +35,14 @@
 
     /** Distribution used to compute inference statistics. */
     private TDistribution distribution;
-    
+
     /**
      * Default constructor.
      */
     public TTestImpl() {
         this(new TDistributionImpl(1.0));
     }
-    
+
     /**
      * Create a test instance using the given distribution for computing
      * inference statistics.
@@ -53,13 +53,13 @@
         super();
         setDistribution(t);
     }
-    
+
     /**
-     * Computes a paired, 2-sample t-statistic based on the data in the input 
+     * Computes a paired, 2-sample t-statistic based on the data in the input
      * arrays.  The t-statistic returned is equivalent to what would be returned by
      * computing the one-sample t-statistic {@link #t(double, double[])}, with
-     * <code>mu = 0</code> and the sample array consisting of the (signed) 
-     * differences between corresponding entries in <code>sample1</code> and 
+     * <code>mu = 0</code> and the sample array consisting of the (signed)
+     * differences between corresponding entries in <code>sample1</code> and
      * <code>sample2.</code>
      * <p>
      * <strong>Preconditions</strong>: <ul>
@@ -79,30 +79,30 @@
         checkSampleData(sample1);
         checkSampleData(sample2);
         double meanDifference = StatUtils.meanDifference(sample1, sample2);
-        return t(meanDifference, 0,  
+        return t(meanDifference, 0,
                 StatUtils.varianceDifference(sample1, sample2, meanDifference),
                 sample1.length);
     }
 
      /**
-     * Returns the <i>observed significance level</i>, or 
-     * <i> p-value</i>, associated with a paired, two-sample, two-tailed t-test 
+     * Returns the <i>observed significance level</i>, or
+     * <i> p-value</i>, associated with a paired, two-sample, two-tailed t-test
      * based on the data in the input arrays.
      * <p>
      * The number returned is the smallest significance level
      * at which one can reject the null hypothesis that the mean of the paired
-     * differences is 0 in favor of the two-sided alternative that the mean paired 
-     * difference is not equal to 0. For a one-sided test, divide the returned 
+     * differences is 0 in favor of the two-sided alternative that the mean paired
+     * difference is not equal to 0. For a one-sided test, divide the returned
      * value by 2.</p>
      * <p>
      * This test is equivalent to a one-sample t-test computed using
      * {@link #tTest(double, double[])} with <code>mu = 0</code> and the sample
-     * array consisting of the signed differences between corresponding elements of 
+     * array consisting of the signed differences between corresponding elements of
      * <code>sample1</code> and <code>sample2.</code></p>
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the p-value depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
      * here</a></p>
      * <p>
@@ -120,30 +120,30 @@
     public double pairedTTest(double[] sample1, double[] sample2)
         throws IllegalArgumentException, MathException {
         double meanDifference = StatUtils.meanDifference(sample1, sample2);
-        return tTest(meanDifference, 0, 
-                StatUtils.varianceDifference(sample1, sample2, meanDifference), 
+        return tTest(meanDifference, 0,
+                StatUtils.varianceDifference(sample1, sample2, meanDifference),
                 sample1.length);
     }
 
      /**
-     * Performs a paired t-test evaluating the null hypothesis that the 
+     * Performs a paired t-test evaluating the null hypothesis that the
      * mean of the paired differences between <code>sample1</code> and
-     * <code>sample2</code> is 0 in favor of the two-sided alternative that the 
-     * mean paired difference is not equal to 0, with significance level 
+     * <code>sample2</code> is 0 in favor of the two-sided alternative that the
+     * mean paired difference is not equal to 0, with significance level
      * <code>alpha</code>.
      * <p>
-     * Returns <code>true</code> iff the null hypothesis can be rejected with 
-     * confidence <code>1 - alpha</code>.  To perform a 1-sided test, use 
+     * Returns <code>true</code> iff the null hypothesis can be rejected with
+     * confidence <code>1 - alpha</code>.  To perform a 1-sided test, use
      * <code>alpha * 2</code></p>
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the test depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
      * here</a></p>
      * <p>
      * <strong>Preconditions</strong>: <ul>
-     * <li>The input array lengths must be the same and their common length 
+     * <li>The input array lengths must be the same and their common length
      * must be at least 2.
      * </li>
      * <li> <code> 0 < alpha < 0.5 </code>
@@ -152,7 +152,7 @@
      * @param sample1 array of sample data values
      * @param sample2 array of sample data values
      * @param alpha significance level of the test
-     * @return true if the null hypothesis can be rejected with 
+     * @return true if the null hypothesis can be rejected with
      * confidence 1 - alpha
      * @throws IllegalArgumentException if the preconditions are not met
      * @throws MathException if an error occurs performing the test
@@ -164,7 +164,7 @@
     }
 
     /**
-     * Computes a <a href="http://www.itl.nist.gov/div898/handbook/prc/section2/prc22.htm#formula"> 
+     * Computes a <a href="http://www.itl.nist.gov/div898/handbook/prc/section2/prc22.htm#formula">
      * t statistic </a> given observed values and a comparison constant.
      * <p>
      * This statistic can be used to perform a one sample t-test for the mean.
@@ -187,7 +187,7 @@
 
     /**
      * Computes a <a href="http://www.itl.nist.gov/div898/handbook/prc/section2/prc22.htm#formula">
-     * t statistic </a> to use in comparing the mean of the dataset described by 
+     * t statistic </a> to use in comparing the mean of the dataset described by
      * <code>sampleStats</code> to <code>mu</code>.
      * <p>
      * This statistic can be used to perform a one sample t-test for the mean.
@@ -209,7 +209,7 @@
     }
 
     /**
-     * Computes a 2-sample t statistic,  under the hypothesis of equal 
+     * Computes a 2-sample t statistic,  under the hypothesis of equal
      * subpopulation variances.  To compute a t-statistic without the
      * equal variances hypothesis, use {@link #t(double[], double[])}.
      * <p>
@@ -220,15 +220,15 @@
      * <p>
      * &nbsp;&nbsp;<code>  t = (m1 - m2) / (sqrt(1/n1 +1/n2) sqrt(var))</code>
      * </p><p>
-     * where <strong><code>n1</code></strong> is the size of first sample; 
-     * <strong><code> n2</code></strong> is the size of second sample; 
-     * <strong><code> m1</code></strong> is the mean of first sample;  
+     * where <strong><code>n1</code></strong> is the size of first sample;
+     * <strong><code> n2</code></strong> is the size of second sample;
+     * <strong><code> m1</code></strong> is the mean of first sample;
      * <strong><code> m2</code></strong> is the mean of second sample</li>
      * </ul>
      * and <strong><code>var</code></strong> is the pooled variance estimate:
      * </p><p>
      * <code>var = sqrt(((n1 - 1)var1 + (n2 - 1)var2) / ((n1-1) + (n2-1)))</code>
-     * </p><p> 
+     * </p><p>
      * with <strong><code>var1<code></strong> the variance of the first sample and
      * <strong><code>var2</code></strong> the variance of the second sample.
      * </p><p>
@@ -249,7 +249,7 @@
                 StatUtils.variance(sample1), StatUtils.variance(sample2),
                 sample1.length, sample2.length);
     }
-    
+
     /**
      * Computes a 2-sample t statistic, without the hypothesis of equal
      * subpopulation variances.  To compute a t-statistic assuming equal
@@ -263,11 +263,11 @@
      * &nbsp;&nbsp; <code>  t = (m1 - m2) / sqrt(var1/n1 + var2/n2)</code>
      * </p><p>
      *  where <strong><code>n1</code></strong> is the size of the first sample
-     * <strong><code> n2</code></strong> is the size of the second sample; 
-     * <strong><code> m1</code></strong> is the mean of the first sample;  
+     * <strong><code> n2</code></strong> is the size of the second sample;
+     * <strong><code> m1</code></strong> is the mean of the first sample;
      * <strong><code> m2</code></strong> is the mean of the second sample;
      * <strong><code> var1</code></strong> is the variance of the first sample;
-     * <strong><code> var2</code></strong> is the variance of the second sample;  
+     * <strong><code> var2</code></strong> is the variance of the second sample;
      * </p><p>
      * <strong>Preconditions</strong>: <ul>
      * <li>The observed array lengths must both be at least 2.
@@ -290,7 +290,7 @@
     /**
      * Computes a 2-sample t statistic </a>, comparing the means of the datasets
      * described by two {@link StatisticalSummary} instances, without the
-     * assumption of equal subpopulation variances.  Use 
+     * assumption of equal subpopulation variances.  Use
      * {@link #homoscedasticT(StatisticalSummary, StatisticalSummary)} to
      * compute a t-statistic under the equal variances assumption.
      * <p>
@@ -301,11 +301,11 @@
      * <p>
      * &nbsp;&nbsp; <code>  t = (m1 - m2) / sqrt(var1/n1 + var2/n2)</code>
      * </p><p>
-     * where <strong><code>n1</code></strong> is the size of the first sample; 
-     * <strong><code> n2</code></strong> is the size of the second sample; 
-     * <strong><code> m1</code></strong> is the mean of the first sample;  
+     * where <strong><code>n1</code></strong> is the size of the first sample;
+     * <strong><code> n2</code></strong> is the size of the second sample;
+     * <strong><code> m1</code></strong> is the mean of the first sample;
      * <strong><code> m2</code></strong> is the mean of the second sample
-     * <strong><code> var1</code></strong> is the variance of the first sample;  
+     * <strong><code> var1</code></strong> is the variance of the first sample;
      * <strong><code> var2</code></strong> is the variance of the second sample
      * </p><p>
      * <strong>Preconditions</strong>: <ul>
@@ -318,21 +318,21 @@
      * @return t statistic
      * @throws IllegalArgumentException if the precondition is not met
      */
-    public double t(StatisticalSummary sampleStats1, 
+    public double t(StatisticalSummary sampleStats1,
                     StatisticalSummary sampleStats2)
     throws IllegalArgumentException {
         checkSampleData(sampleStats1);
         checkSampleData(sampleStats2);
-        return t(sampleStats1.getMean(), sampleStats2.getMean(), 
+        return t(sampleStats1.getMean(), sampleStats2.getMean(),
                 sampleStats1.getVariance(), sampleStats2.getVariance(),
                 sampleStats1.getN(), sampleStats2.getN());
     }
-    
+
     /**
      * Computes a 2-sample t statistic, comparing the means of the datasets
      * described by two {@link StatisticalSummary} instances, under the
      * assumption of equal subpopulation variances.  To compute a t-statistic
-     * without the equal variances assumption, use 
+     * without the equal variances assumption, use
      * {@link #t(StatisticalSummary, StatisticalSummary)}.
      * <p>
      * This statistic can be used to perform a (homoscedastic) two-sample
@@ -342,14 +342,14 @@
      * <p>
      * &nbsp;&nbsp;<code>  t = (m1 - m2) / (sqrt(1/n1 +1/n2) sqrt(var))</code>
      * </p><p>
-     * where <strong><code>n1</code></strong> is the size of first sample; 
-     * <strong><code> n2</code></strong> is the size of second sample; 
-     * <strong><code> m1</code></strong> is the mean of first sample;  
+     * where <strong><code>n1</code></strong> is the size of first sample;
+     * <strong><code> n2</code></strong> is the size of second sample;
+     * <strong><code> m1</code></strong> is the mean of first sample;
      * <strong><code> m2</code></strong> is the mean of second sample
      * and <strong><code>var</code></strong> is the pooled variance estimate:
      * </p><p>
      * <code>var = sqrt(((n1 - 1)var1 + (n2 - 1)var2) / ((n1-1) + (n2-1)))</code>
-     * <p> 
+     * <p>
      * with <strong><code>var1<code></strong> the variance of the first sample and
      * <strong><code>var2</code></strong> the variance of the second sample.
      * </p><p>
@@ -363,30 +363,30 @@
      * @return t statistic
      * @throws IllegalArgumentException if the precondition is not met
      */
-    public double homoscedasticT(StatisticalSummary sampleStats1, 
+    public double homoscedasticT(StatisticalSummary sampleStats1,
             StatisticalSummary sampleStats2)
     throws IllegalArgumentException {
         checkSampleData(sampleStats1);
         checkSampleData(sampleStats2);
-        return homoscedasticT(sampleStats1.getMean(), sampleStats2.getMean(), 
-                sampleStats1.getVariance(), sampleStats2.getVariance(), 
+        return homoscedasticT(sampleStats1.getMean(), sampleStats2.getMean(),
+                sampleStats1.getVariance(), sampleStats2.getVariance(),
                 sampleStats1.getN(), sampleStats2.getN());
     }
 
      /**
-     * Returns the <i>observed significance level</i>, or 
-     * <i>p-value</i>, associated with a one-sample, two-tailed t-test 
+     * Returns the <i>observed significance level</i>, or
+     * <i>p-value</i>, associated with a one-sample, two-tailed t-test
      * comparing the mean of the input array with the constant <code>mu</code>.
      * <p>
      * The number returned is the smallest significance level
-     * at which one can reject the null hypothesis that the mean equals 
+     * at which one can reject the null hypothesis that the mean equals
      * <code>mu</code> in favor of the two-sided alternative that the mean
-     * is different from <code>mu</code>. For a one-sided test, divide the 
+     * is different from <code>mu</code>. For a one-sided test, divide the
      * returned value by 2.</p>
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the test depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">here</a>
      * </p><p>
      * <strong>Preconditions</strong>: <ul>
@@ -411,8 +411,8 @@
      * two-sided t-test</a> evaluating the null hypothesis that the mean of the population from
      * which <code>sample</code> is drawn equals <code>mu</code>.
      * <p>
-     * Returns <code>true</code> iff the null hypothesis can be 
-     * rejected with confidence <code>1 - alpha</code>.  To 
+     * Returns <code>true</code> iff the null hypothesis can be
+     * rejected with confidence <code>1 - alpha</code>.  To
      * perform a 1-sided test, use <code>alpha * 2</code>
      * </p><p>
      * <strong>Examples:</strong><br><ol>
@@ -420,14 +420,14 @@
      * the 95% level, use <br><code>tTest(mu, sample, 0.05) </code>
      * </li>
      * <li>To test the (one-sided) hypothesis <code> sample mean < mu </code>
-     * at the 99% level, first verify that the measured sample mean is less 
-     * than <code>mu</code> and then use 
+     * at the 99% level, first verify that the measured sample mean is less
+     * than <code>mu</code> and then use
      * <br><code>tTest(mu, sample, 0.02) </code>
      * </li></ol></p>
      * <p>
      * <strong>Usage Note:</strong><br>
-     * The validity of the test depends on the assumptions of the one-sample 
-     * parametric t-test procedure, as discussed 
+     * The validity of the test depends on the assumptions of the one-sample
+     * parametric t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/sg_glos.html#one-sample">here</a>
      * </p><p>
      * <strong>Preconditions</strong>: <ul>
@@ -448,20 +448,20 @@
     }
 
     /**
-     * Returns the <i>observed significance level</i>, or 
-     * <i>p-value</i>, associated with a one-sample, two-tailed t-test 
+     * Returns the <i>observed significance level</i>, or
+     * <i>p-value</i>, associated with a one-sample, two-tailed t-test
      * comparing the mean of the dataset described by <code>sampleStats</code>
      * with the constant <code>mu</code>.
      * <p>
      * The number returned is the smallest significance level
-     * at which one can reject the null hypothesis that the mean equals 
+     * at which one can reject the null hypothesis that the mean equals
      * <code>mu</code> in favor of the two-sided alternative that the mean
-     * is different from <code>mu</code>. For a one-sided test, divide the 
+     * is different from <code>mu</code>. For a one-sided test, divide the
      * returned value by 2.</p>
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the test depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
      * here</a></p>
      * <p>
@@ -497,14 +497,14 @@
      * the 95% level, use <br><code>tTest(mu, sampleStats, 0.05) </code>
      * </li>
      * <li>To test the (one-sided) hypothesis <code> sample mean < mu </code>
-     * at the 99% level, first verify that the measured sample mean is less 
-     * than <code>mu</code> and then use 
+     * at the 99% level, first verify that the measured sample mean is less
+     * than <code>mu</code> and then use
      * <br><code>tTest(mu, sampleStats, 0.02) </code>
      * </li></ol></p>
      * <p>
      * <strong>Usage Note:</strong><br>
-     * The validity of the test depends on the assumptions of the one-sample 
-     * parametric t-test procedure, as discussed 
+     * The validity of the test depends on the assumptions of the one-sample
+     * parametric t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/sg_glos.html#one-sample">here</a>
      * </p><p>
      * <strong>Preconditions</strong>: <ul>
@@ -526,28 +526,28 @@
     }
 
     /**
-     * Returns the <i>observed significance level</i>, or 
-     * <i>p-value</i>, associated with a two-sample, two-tailed t-test 
+     * Returns the <i>observed significance level</i>, or
+     * <i>p-value</i>, associated with a two-sample, two-tailed t-test
      * comparing the means of the input arrays.
      * <p>
      * The number returned is the smallest significance level
      * at which one can reject the null hypothesis that the two means are
-     * equal in favor of the two-sided alternative that they are different. 
+     * equal in favor of the two-sided alternative that they are different.
      * For a one-sided test, divide the returned value by 2.</p>
      * <p>
      * The test does not assume that the underlying popuation variances are
-     * equal  and it uses approximated degrees of freedom computed from the 
+     * equal  and it uses approximated degrees of freedom computed from the
      * sample data to compute the p-value.  The t-statistic used is as defined in
      * {@link #t(double[], double[])} and the Welch-Satterthwaite approximation
-     * to the degrees of freedom is used, 
-     * as described 
+     * to the degrees of freedom is used,
+     * as described
      * <a href="http://www.itl.nist.gov/div898/handbook/prc/section3/prc31.htm">
      * here.</a>  To perform the test under the assumption of equal subpopulation
      * variances, use {@link #homoscedasticTTest(double[], double[])}.</p>
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the p-value depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
      * here</a></p>
      * <p>
@@ -569,10 +569,10 @@
                 StatUtils.variance(sample1), StatUtils.variance(sample2),
                 sample1.length, sample2.length);
     }
-    
+
     /**
-     * Returns the <i>observed significance level</i>, or 
-     * <i>p-value</i>, associated with a two-sample, two-tailed t-test 
+     * Returns the <i>observed significance level</i>, or
+     * <i>p-value</i>, associated with a two-sample, two-tailed t-test
      * comparing the means of the input arrays, under the assumption that
      * the two samples are drawn from subpopulations with equal variances.
      * To perform the test without the equal variances assumption, use
@@ -580,7 +580,7 @@
      * <p>
      * The number returned is the smallest significance level
      * at which one can reject the null hypothesis that the two means are
-     * equal in favor of the two-sided alternative that they are different. 
+     * equal in favor of the two-sided alternative that they are different.
      * For a one-sided test, divide the returned value by 2.</p>
      * <p>
      * A pooled variance estimate is used to compute the t-statistic.  See
@@ -589,7 +589,7 @@
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the p-value depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
      * here</a></p>
      * <p>
@@ -607,47 +607,47 @@
     throws IllegalArgumentException, MathException {
         checkSampleData(sample1);
         checkSampleData(sample2);
-        return homoscedasticTTest(StatUtils.mean(sample1), 
+        return homoscedasticTTest(StatUtils.mean(sample1),
                 StatUtils.mean(sample2), StatUtils.variance(sample1),
-                StatUtils.variance(sample2), sample1.length, 
+                StatUtils.variance(sample2), sample1.length,
                 sample2.length);
     }
-    
+
 
      /**
-     * Performs a 
+     * Performs a
      * <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm">
-     * two-sided t-test</a> evaluating the null hypothesis that <code>sample1</code> 
-     * and <code>sample2</code> are drawn from populations with the same mean, 
+     * two-sided t-test</a> evaluating the null hypothesis that <code>sample1</code>
+     * and <code>sample2</code> are drawn from populations with the same mean,
      * with significance level <code>alpha</code>.  This test does not assume
      * that the subpopulation variances are equal.  To perform the test assuming
-     * equal variances, use 
+     * equal variances, use
      * {@link #homoscedasticTTest(double[], double[], double)}.
      * <p>
      * Returns <code>true</code> iff the null hypothesis that the means are
-     * equal can be rejected with confidence <code>1 - alpha</code>.  To 
+     * equal can be rejected with confidence <code>1 - alpha</code>.  To
      * perform a 1-sided test, use <code>alpha / 2</code></p>
      * <p>
      * See {@link #t(double[], double[])} for the formula used to compute the
      * t-statistic.  Degrees of freedom are approximated using the
      * <a href="http://www.itl.nist.gov/div898/handbook/prc/section3/prc31.htm">
      * Welch-Satterthwaite approximation.</a></p>
-      
+
      * <p>
      * <strong>Examples:</strong><br><ol>
      * <li>To test the (2-sided) hypothesis <code>mean 1 = mean 2 </code> at
-     * the 95% level,  use 
+     * the 95% level,  use
      * <br><code>tTest(sample1, sample2, 0.05). </code>
      * </li>
      * <li>To test the (one-sided) hypothesis <code> mean 1 < mean 2 </code> at
      * the 99% level, first verify that the measured  mean of <code>sample 1</code>
-     * is less than the mean of <code>sample 2</code> and then use 
+     * is less than the mean of <code>sample 2</code> and then use
      * <br><code>tTest(sample1, sample2, 0.02) </code>
      * </li></ol></p>
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the test depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
      * here</a></p>
      * <p>
@@ -660,7 +660,7 @@
      * @param sample1 array of sample data values
      * @param sample2 array of sample data values
      * @param alpha significance level of the test
-     * @return true if the null hypothesis can be rejected with 
+     * @return true if the null hypothesis can be rejected with
      * confidence 1 - alpha
      * @throws IllegalArgumentException if the preconditions are not met
      * @throws MathException if an error occurs performing the test
@@ -671,21 +671,21 @@
         checkSignificanceLevel(alpha);
         return (tTest(sample1, sample2) < alpha);
     }
-    
+
     /**
-     * Performs a 
+     * Performs a
      * <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm">
-     * two-sided t-test</a> evaluating the null hypothesis that <code>sample1</code> 
-     * and <code>sample2</code> are drawn from populations with the same mean, 
+     * two-sided t-test</a> evaluating the null hypothesis that <code>sample1</code>
+     * and <code>sample2</code> are drawn from populations with the same mean,
      * with significance level <code>alpha</code>,  assuming that the
-     * subpopulation variances are equal.  Use 
+     * subpopulation variances are equal.  Use
      * {@link #tTest(double[], double[], double)} to perform the test without
      * the assumption of equal variances.
      * <p>
      * Returns <code>true</code> iff the null hypothesis that the means are
-     * equal can be rejected with confidence <code>1 - alpha</code>.  To 
+     * equal can be rejected with confidence <code>1 - alpha</code>.  To
      * perform a 1-sided test, use <code>alpha * 2.</code>  To perform the test
-     * without the assumption of equal subpopulation variances, use 
+     * without the assumption of equal subpopulation variances, use
      * {@link #tTest(double[], double[], double)}.</p>
      * <p>
      * A pooled variance estimate is used to compute the t-statistic. See
@@ -697,7 +697,7 @@
      * the 95% level, use <br><code>tTest(sample1, sample2, 0.05). </code>
      * </li>
      * <li>To test the (one-sided) hypothesis <code> mean 1 < mean 2, </code>
-     * at the 99% level, first verify that the measured mean of 
+     * at the 99% level, first verify that the measured mean of
      * <code>sample 1</code> is less than the mean of <code>sample 2</code>
      * and then use
      * <br><code>tTest(sample1, sample2, 0.02) </code>
@@ -705,7 +705,7 @@
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the test depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
      * here</a></p>
      * <p>
@@ -718,7 +718,7 @@
      * @param sample1 array of sample data values
      * @param sample2 array of sample data values
      * @param alpha significance level of the test
-     * @return true if the null hypothesis can be rejected with 
+     * @return true if the null hypothesis can be rejected with
      * confidence 1 - alpha
      * @throws IllegalArgumentException if the preconditions are not met
      * @throws MathException if an error occurs performing the test
@@ -731,25 +731,25 @@
     }
 
      /**
-     * Returns the <i>observed significance level</i>, or 
-     * <i>p-value</i>, associated with a two-sample, two-tailed t-test 
+     * Returns the <i>observed significance level</i>, or
+     * <i>p-value</i>, associated with a two-sample, two-tailed t-test
      * comparing the means of the datasets described by two StatisticalSummary
      * instances.
      * <p>
      * The number returned is the smallest significance level
      * at which one can reject the null hypothesis that the two means are
-     * equal in favor of the two-sided alternative that they are different. 
+     * equal in favor of the two-sided alternative that they are different.
      * For a one-sided test, divide the returned value by 2.</p>
      * <p>
      * The test does not assume that the underlying popuation variances are
-     * equal  and it uses approximated degrees of freedom computed from the 
+     * equal  and it uses approximated degrees of freedom computed from the
      * sample data to compute the p-value.   To perform the test assuming
-     * equal variances, use 
+     * equal variances, use
      * {@link #homoscedasticTTest(StatisticalSummary, StatisticalSummary)}.</p>
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the p-value depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
      * here</a></p>
      * <p>
@@ -769,13 +769,13 @@
         checkSampleData(sampleStats1);
         checkSampleData(sampleStats2);
         return tTest(sampleStats1.getMean(), sampleStats2.getMean(), sampleStats1.getVariance(),
-                sampleStats2.getVariance(), sampleStats1.getN(), 
+                sampleStats2.getVariance(), sampleStats1.getN(),
                 sampleStats2.getN());
     }
-    
+
     /**
-     * Returns the <i>observed significance level</i>, or 
-     * <i>p-value</i>, associated with a two-sample, two-tailed t-test 
+     * Returns the <i>observed significance level</i>, or
+     * <i>p-value</i>, associated with a two-sample, two-tailed t-test
      * comparing the means of the datasets described by two StatisticalSummary
      * instances, under the hypothesis of equal subpopulation variances. To
      * perform a test without the equal variances assumption, use
@@ -783,7 +783,7 @@
      * <p>
      * The number returned is the smallest significance level
      * at which one can reject the null hypothesis that the two means are
-     * equal in favor of the two-sided alternative that they are different. 
+     * equal in favor of the two-sided alternative that they are different.
      * For a one-sided test, divide the returned value by 2.</p>
      * <p>
      * See {@link #homoscedasticT(double[], double[])} for the formula used to
@@ -792,7 +792,7 @@
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the p-value depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">here</a>
      * </p><p>
      * <strong>Preconditions</strong>: <ul>
@@ -806,21 +806,21 @@
      * @throws IllegalArgumentException if the precondition is not met
      * @throws MathException if an error occurs computing the p-value
      */
-    public double homoscedasticTTest(StatisticalSummary sampleStats1, 
+    public double homoscedasticTTest(StatisticalSummary sampleStats1,
                                      StatisticalSummary sampleStats2)
     throws IllegalArgumentException, MathException {
         checkSampleData(sampleStats1);
         checkSampleData(sampleStats2);
         return homoscedasticTTest(sampleStats1.getMean(),
                 sampleStats2.getMean(), sampleStats1.getVariance(),
-                sampleStats2.getVariance(), sampleStats1.getN(), 
+                sampleStats2.getVariance(), sampleStats1.getN(),
                 sampleStats2.getN());
     }
 
     /**
-     * Performs a 
+     * Performs a
      * <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm">
-     * two-sided t-test</a> evaluating the null hypothesis that 
+     * two-sided t-test</a> evaluating the null hypothesis that
      * <code>sampleStats1</code> and <code>sampleStats2</code> describe
      * datasets drawn from populations with the same mean, with significance
      * level <code>alpha</code>.   This test does not assume that the
@@ -829,7 +829,7 @@
      * {@link #homoscedasticTTest(StatisticalSummary, StatisticalSummary)}.
      * <p>
      * Returns <code>true</code> iff the null hypothesis that the means are
-     * equal can be rejected with confidence <code>1 - alpha</code>.  To 
+     * equal can be rejected with confidence <code>1 - alpha</code>.  To
      * perform a 1-sided test, use <code>alpha * 2</code></p>
      * <p>
      * See {@link #t(double[], double[])} for the formula used to compute the
@@ -839,19 +839,19 @@
      * <p>
      * <strong>Examples:</strong><br><ol>
      * <li>To test the (2-sided) hypothesis <code>mean 1 = mean 2 </code> at
-     * the 95%, use 
+     * the 95%, use
      * <br><code>tTest(sampleStats1, sampleStats2, 0.05) </code>
      * </li>
      * <li>To test the (one-sided) hypothesis <code> mean 1 < mean 2 </code>
-     * at the 99% level,  first verify that the measured mean of  
+     * at the 99% level,  first verify that the measured mean of
      * <code>sample 1</code> is less than  the mean of <code>sample 2</code>
-     * and then use 
+     * and then use
      * <br><code>tTest(sampleStats1, sampleStats2, 0.02) </code>
      * </li></ol></p>
      * <p>
      * <strong>Usage Note:</strong><br>
      * The validity of the test depends on the assumptions of the parametric
-     * t-test procedure, as discussed 
+     * t-test procedure, as discussed
      * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
      * here</a></p>
      * <p>
@@ -865,7 +865,7 @@
      * @param sampleStats1 StatisticalSummary describing sample data values
      * @param sampleStats2 StatisticalSummary describing sample data values
      * @param alpha significance level of the test
-     * @return true if the null hypothesis can be rejected with 
+     * @return true if the null hypothesis can be rejected with
      * confidence 1 - alpha
      * @throws IllegalArgumentException if the preconditions are not met
      * @throws MathException if an error occurs performing the test
@@ -876,12 +876,12 @@
         checkSignificanceLevel(alpha);
         return (tTest(sampleStats1, sampleStats2) < alpha);
     }
-    
-    //----------------------------------------------- Protected methods 
+
+    //----------------------------------------------- Protected methods
 
     /**
      * Computes approximate degrees of freedom for 2-sample t-test.
-     * 
+     *
      * @param v1 first sample variance
      * @param v2 second sample variance
      * @param n1 first sample n
@@ -896,7 +896,7 @@
 
     /**
      * Computes t test statistic for 1-sample t-test.
-     * 
+     *
      * @param m sample mean
      * @param mu constant to test against
      * @param v sample variance
@@ -906,12 +906,12 @@
     protected double t(double m, double mu, double v, double n) {
         return (m - mu) / Math.sqrt(v / n);
     }
-    
+
     /**
      * Computes t test statistic for 2-sample t-test.
      * <p>
      * Does not assume that subpopulation variances are equal.</p>
-     * 
+     *
      * @param m1 first sample mean
      * @param m2 second sample mean
      * @param v1 first sample variance
@@ -924,11 +924,11 @@
             double n2)  {
             return (m1 - m2) / Math.sqrt((v1 / n1) + (v2 / n2));
     }
-    
+
     /**
      * Computes t test statistic for 2-sample t-test under the hypothesis
      * of equal subpopulation variances.
-     * 
+     *
      * @param m1 first sample mean
      * @param m2 second sample mean
      * @param v1 first sample variance
@@ -939,13 +939,13 @@
      */
     protected double homoscedasticT(double m1, double m2,  double v1,
             double v2, double n1, double n2)  {
-            double pooledVariance = ((n1  - 1) * v1 + (n2 -1) * v2 ) / (n1 + n2 - 2); 
+            double pooledVariance = ((n1  - 1) * v1 + (n2 -1) * v2 ) / (n1 + n2 - 2);
             return (m1 - m2) / Math.sqrt(pooledVariance * (1d / n1 + 1d / n2));
     }
-    
+
     /**
      * Computes p-value for 2-sided, 1-sample t-test.
-     * 
+     *
      * @param m sample mean
      * @param mu constant to test against
      * @param v sample variance
@@ -965,7 +965,7 @@
      * <p>
      * Does not assume subpopulation variances are equal. Degrees of freedom
      * are estimated from the data.</p>
-     * 
+     *
      * @param m1 first sample mean
      * @param m2 second sample mean
      * @param v1 first sample variance
@@ -975,7 +975,7 @@
      * @return p-value
      * @throws MathException if an error occurs computing the p-value
      */
-    protected double tTest(double m1, double m2, double v1, double v2, 
+    protected double tTest(double m1, double m2, double v1, double v2,
             double n1, double n2)
     throws MathException {
         double t = Math.abs(t(m1, m2, v1, v2, n1, n2));
@@ -984,13 +984,13 @@
         distribution.setDegreesOfFreedom(degreesOfFreedom);
         return 2.0 * distribution.cumulativeProbability(-t);
     }
-    
+
     /**
      * Computes p-value for 2-sided, 2-sample t-test, under the assumption
      * of equal subpopulation variances.
      * <p>
      * The sum of the sample sizes minus 2 is used as degrees of freedom.</p>
-     * 
+     *
      * @param m1 first sample mean
      * @param m2 second sample mean
      * @param v1 first sample variance
@@ -1008,7 +1008,7 @@
         distribution.setDegreesOfFreedom(degreesOfFreedom);
         return 2.0 * distribution.cumulativeProbability(-t);
     }
-    
+
     /**
      * Modify the distribution used to compute inference statistics.
      * @param value the new distribution

Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/TestUtils.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/TestUtils.java?rev=811685&r1=811684&r2=811685&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/TestUtils.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/TestUtils.java Sat Sep  5 17:36:48 2009
@@ -25,7 +25,7 @@
  * perform inference tests.
  *
  * @since 1.1
- * @version $Revision$ $Date$ 
+ * @version $Revision$ $Date$
  */
 public class TestUtils  {
     /**
@@ -34,100 +34,100 @@
     protected TestUtils() {
         super();
     }
-    
+
     /** Singleton TTest instance using default implementation. */
     private static TTest tTest = new TTestImpl();
-   
+
     /** Singleton ChiSquareTest instance using default implementation. */
-    private static ChiSquareTest chiSquareTest = 
+    private static ChiSquareTest chiSquareTest =
         new ChiSquareTestImpl();
-    
+
     /** Singleton ChiSquareTest instance using default implementation. */
-    private static UnknownDistributionChiSquareTest unknownDistributionChiSquareTest = 
+    private static UnknownDistributionChiSquareTest unknownDistributionChiSquareTest =
         new ChiSquareTestImpl();
-    
+
     /** Singleton OneWayAnova instance using default implementation. */
     private static OneWayAnova oneWayAnova =
         new OneWayAnovaImpl();
-    
+
     /**
      * Set the (singleton) TTest instance.
-     * 
+     *
      * @param chiSquareTest the new instance to use
      * @since 1.2
      */
     public static void setChiSquareTest(TTest chiSquareTest) {
         TestUtils.tTest = chiSquareTest;
     }
-    
+
     /**
      * Return a (singleton) TTest instance.  Does not create a new instance.
-     * 
+     *
      * @return a TTest instance
      */
     public static TTest getTTest() {
         return tTest;
     }
-    
+
     /**
      * Set the (singleton) ChiSquareTest instance.
-     * 
+     *
      * @param chiSquareTest the new instance to use
      * @since 1.2
      */
     public static void setChiSquareTest(ChiSquareTest chiSquareTest) {
         TestUtils.chiSquareTest = chiSquareTest;
     }
-    
+
     /**
      * Return a (singleton) ChiSquareTest instance.  Does not create a new instance.
-     * 
+     *
      * @return a ChiSquareTest instance
      */
     public static ChiSquareTest getChiSquareTest() {
         return chiSquareTest;
     }
-    
+
     /**
      * Set the (singleton) UnknownDistributionChiSquareTest instance.
-     * 
+     *
      * @param unknownDistributionChiSquareTest the new instance to use
      * @since 1.2
      */
     public static void setUnknownDistributionChiSquareTest(UnknownDistributionChiSquareTest unknownDistributionChiSquareTest) {
         TestUtils.unknownDistributionChiSquareTest = unknownDistributionChiSquareTest;
     }
-    
+
     /**
      * Return a (singleton) UnknownDistributionChiSquareTest instance.  Does not create a new instance.
-     * 
+     *
      * @return a UnknownDistributionChiSquareTest instance
      */
     public static UnknownDistributionChiSquareTest getUnknownDistributionChiSquareTest() {
         return unknownDistributionChiSquareTest;
     }
-    
+
     /**
      * Set the (singleton) OneWayAnova instance
-     * 
+     *
      * @param oneWayAnova the new instance to use
      * @since 1.2
      */
     public static void setOneWayAnova(OneWayAnova oneWayAnova) {
         TestUtils.oneWayAnova = oneWayAnova;
     }
-    
+
     /**
      * Return a (singleton) OneWayAnova instance.  Does not create a new instance.
-     * 
+     *
      * @return a OneWayAnova instance
      * @since 1.2
      */
     public static OneWayAnova getOneWayAnova() {
         return oneWayAnova;
     }
-    
-    
+
+
     // CHECKSTYLE: stop JavadocMethodCheck
 
     /**
@@ -309,7 +309,7 @@
     /**
      * @see org.apache.commons.math.stat.inference.ChiSquareTest#chiSquare(long[][])
      */
-    public static double chiSquare(long[][] counts) 
+    public static double chiSquare(long[][] counts)
         throws IllegalArgumentException {
         return chiSquareTest.chiSquare(counts);
     }
@@ -378,7 +378,7 @@
         throws IllegalArgumentException, MathException {
         return unknownDistributionChiSquareTest.chiSquareTestDataSetsComparison(observed1, observed2, alpha);
     }
-    
+
     /**
      * @see org.apache.commons.math.stat.inference.OneWayAnova#anovaFValue(Collection)
      *
@@ -388,17 +388,17 @@
     throws IllegalArgumentException, MathException {
         return oneWayAnova.anovaFValue(categoryData);
     }
-    
+
     /**
      * @see org.apache.commons.math.stat.inference.OneWayAnova#anovaPValue(Collection)
-     * 
+     *
      * @since 1.2
      */
     public static double oneWayAnovaPValue(Collection<double[]> categoryData)
     throws IllegalArgumentException, MathException {
         return oneWayAnova.anovaPValue(categoryData);
     }
-    
+
     /**
      * @see org.apache.commons.math.stat.inference.OneWayAnova#anovaTest(Collection,double)
      *

Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/UnknownDistributionChiSquareTest.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/UnknownDistributionChiSquareTest.java?rev=811685&r1=811684&r2=811685&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/UnknownDistributionChiSquareTest.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/UnknownDistributionChiSquareTest.java Sat Sep  5 17:36:48 2009
@@ -24,12 +24,12 @@
  * but provided by one sample. We compare the second sample against the first.</p>
  *
  * @version $Revision$ $Date$
- * @since 1.2 
+ * @since 1.2
  */
 public interface UnknownDistributionChiSquareTest extends ChiSquareTest {
-     
+
     /**
-     * <p>Computes a 
+     * <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
@@ -37,7 +37,7 @@
      * same.  The formula used to compute the test statistic is</p>
      * <code>
      * &sum;[(K * observed1[i] - observed2[i]/K)<sup>2</sup> / (observed1[i] + observed2[i])]
-     * </code> where 
+     * </code> where
      * <br/><code>K = &sqrt;[&sum(observed2 / &sum;(observed1)]</code>
      * </p>
      * <p>This statistic can be used to perform a Chi-Square test evaluating the null hypothesis that
@@ -68,7 +68,7 @@
      * <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 
+     * bin frequency counts in <code>observed1</code> and
      * <code>observed2</code>.
      * </p>
      * <p>The number returned is the smallest significance level at which one
@@ -110,7 +110,7 @@
      * significance level <code>alpha</code>.  Returns true iff the null
      * hypothesis can be rejected with 100 * (1 - alpha) percent confidence.
      * </p>
-     * <p>See {@link #chiSquareDataSetsComparison(long[], long[])} for 
+     * <p>See {@link #chiSquareDataSetsComparison(long[], long[])} 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.

Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/ranking/NaNStrategy.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/ranking/NaNStrategy.java?rev=811685&r1=811684&r2=811685&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/ranking/NaNStrategy.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/ranking/NaNStrategy.java Sat Sep  5 17:36:48 2009
@@ -34,16 +34,16 @@
  * @version $Revision$ $Date$
  */
 public enum NaNStrategy {
-    
+
     /** NaNs are considered minimal in the ordering */
     MINIMAL,
-    
+
     /** NaNs are considered maximal in the ordering */
     MAXIMAL,
-    
+
     /** NaNs are removed before computing ranks */
     REMOVED,
-    
+
     /** NaNs are left in place */
     FIXED
 }

Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/ranking/NaturalRanking.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/ranking/NaturalRanking.java?rev=811685&r1=811684&r2=811685&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/ranking/NaturalRanking.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/ranking/NaturalRanking.java Sat Sep  5 17:36:48 2009
@@ -31,10 +31,10 @@
 /**
  * <p> Ranking based on the natural ordering on doubles.</p>
  * <p>NaNs are treated according to the configured {@link NaNStrategy} and ties
- * are handled using the selected {@link TiesStrategy}. 
+ * are handled using the selected {@link TiesStrategy}.
  * Configuration settings are supplied in optional constructor arguments.
  * Defaults are {@link NaNStrategy#MAXIMAL} and {@link TiesStrategy#AVERAGE},
- * respectively. When using {@link TiesStrategy#RANDOM}, a 
+ * respectively. When using {@link TiesStrategy#RANDOM}, a
  * {@link RandomGenerator} may be supplied as a constructor argument.</p>
  * <p>Examples:
  * <table border="1" cellpadding="3">
@@ -63,27 +63,27 @@
  * <td>MINIMAL</td>
  * <td>MAXIMUM</td>
  * <td>(6, 5, 7, 8, 5, 9, 2, 2, 5)</td></tr></table></p>
- * 
+ *
  * @since 2.0
  * @version $Revision$ $Date$
  */
 public class NaturalRanking implements RankingAlgorithm {
-   
+
     /** NaN strategy - defaults to NaNs maximal */
     private final NaNStrategy nanStrategy;
-    
+
     /** Ties strategy - defaults to ties averaged */
     private final TiesStrategy tiesStrategy;
-    
+
     /** Source of random data - used only when ties strategy is RANDOM */
     private final RandomData randomData;
-    
+
     /** default NaN strategy */
     public static final NaNStrategy DEFAULT_NAN_STRATEGY = NaNStrategy.MAXIMAL;
-    
+
     /** default ties strategy */
     public static final TiesStrategy DEFAULT_TIES_STRATEGY = TiesStrategy.AVERAGE;
-    
+
     /**
      * Create a NaturalRanking with default strategies for handling ties and NaNs.
      */
@@ -96,7 +96,7 @@
 
     /**
      * Create a NaturalRanking with the given TiesStrategy.
-     * 
+     *
      * @param tiesStrategy the TiesStrategy to use
      */
     public NaturalRanking(TiesStrategy tiesStrategy) {
@@ -108,19 +108,19 @@
 
     /**
      * Create a NaturalRanking with the given NaNStrategy.
-     * 
+     *
      * @param nanStrategy the NaNStrategy to use
      */
     public NaturalRanking(NaNStrategy nanStrategy) {
         super();
         this.nanStrategy = nanStrategy;
         tiesStrategy = DEFAULT_TIES_STRATEGY;
-        randomData = null; 
+        randomData = null;
     }
 
     /**
      * Create a NaturalRanking with the given NaNStrategy and TiesStrategy.
-     * 
+     *
      * @param nanStrategy NaNStrategy to use
      * @param tiesStrategy TiesStrategy to use
      */
@@ -130,11 +130,11 @@
         this.tiesStrategy = tiesStrategy;
         randomData = new RandomDataImpl();
     }
-    
+
     /**
      * Create a NaturalRanking with TiesStrategy.RANDOM and the given
      * RandomGenerator as the source of random data.
-     * 
+     *
      * @param randomGenerator source of random data
      */
     public NaturalRanking(RandomGenerator randomGenerator) {
@@ -148,7 +148,7 @@
     /**
      * Create a NaturalRanking with the given NaNStrategy, TiesStrategy.RANDOM
      * and the given source of random data.
-     * 
+     *
      * @param nanStrategy NaNStrategy to use
      * @param randomGenerator source of random data
      */
@@ -159,10 +159,10 @@
         this.tiesStrategy = TiesStrategy.RANDOM;
         randomData = new RandomDataImpl(randomGenerator);
     }
-    
+
     /**
      * Return the NaNStrategy
-     * 
+     *
      * @return returns the NaNStrategy
      */
     public NaNStrategy getNanStrategy() {
@@ -171,7 +171,7 @@
 
     /**
      * Return the TiesStrategy
-     * 
+     *
      * @return the TiesStrategy
      */
     public TiesStrategy getTiesStrategy() {
@@ -182,18 +182,18 @@
      * Rank <code>data</code> using the natural ordering on Doubles, with
      * NaN values handled according to <code>nanStrategy</code> and ties
      * resolved using <code>tiesStrategy.</code>
-     * 
+     *
      * @param data array to be ranked
      * @return array of ranks
      */
     public double[] rank(double[] data) {
-        
+
         // Array recording initial positions of data to be ranked
-        IntDoublePair[] ranks = new IntDoublePair[data.length];  
+        IntDoublePair[] ranks = new IntDoublePair[data.length];
         for (int i = 0; i < data.length; i++) {
             ranks[i] = new IntDoublePair(data[i], i);
         }
-        
+
         // Recode, remove or record positions of NaNs
         List<Integer> nanPositions = null;
         switch (nanStrategy) {
@@ -212,14 +212,14 @@
             default: // this should not happen unless NaNStrategy enum is changed
                 throw MathRuntimeException.createInternalError(null);
         }
-        
+
         // Sort the IntDoublePairs
         Arrays.sort(ranks);
-        
+
         // Walk the sorted array, filling output array using sorted positions,
         // resolving ties as we go
         double[] out = new double[ranks.length];
-        int pos = 1;  // position in sorted array 
+        int pos = 1;  // position in sorted array
         out[ranks[0].getPosition()] = pos;
         List<Integer> tiesTrace = new ArrayList<Integer>();
         tiesTrace.add(ranks[0].getPosition());
@@ -246,11 +246,11 @@
         }
         return out;
     }
-    
+
     /**
      * Returns an array that is a copy of the input array with IntDoublePairs
      * having NaN values removed.
-     * 
+     *
      * @param ranks input array
      * @return array with NaN-valued entries removed
      */
@@ -279,8 +279,8 @@
     }
 
     /**
-     * Recodes NaN values to the given value. 
-     * 
+     * Recodes NaN values to the given value.
+     *
      * @param ranks array to recode
      * @param value the value to replace NaNs with
      */
@@ -292,10 +292,10 @@
             }
         }
     }
-    
+
     /**
      * Checks for presence of NaNs in <code>ranks.</code>
-     * 
+     *
      * @param ranks array to be searched for NaNs
      * @return true iff ranks contains one or more NaNs
      */
@@ -307,7 +307,7 @@
         }
         return false;
     }
-    
+
     /**
      * Resolve a sequence of ties, using the configured {@link TiesStrategy}.
      * The input <code>ranks</code> array is expected to take the same value
@@ -316,20 +316,20 @@
      * tiesTrace = <2,4,7> and tiesStrategy is MINIMUM, ranks will be unchanged.
      * The same array and trace with tiesStrategy AVERAGE will come out
      * <5,8,3,6,3,7,1,3>.
-     * 
-     * @param ranks array of ranks 
+     *
+     * @param ranks array of ranks
      * @param tiesTrace list of indices where <code>ranks</code> is constant
-     * -- that is, for any i and j in TiesTrace, <code> ranks[i] == ranks[j] 
+     * -- that is, for any i and j in TiesTrace, <code> ranks[i] == ranks[j]
      * </code>
      */
     private void resolveTie(double[] ranks, List<Integer> tiesTrace) {
-        
+
         // constant value of ranks over tiesTrace
         final double c = ranks[tiesTrace.get(0)];
-        
+
         // length of sequence of tied ranks
         final int length = tiesTrace.size();
-        
+
         switch (tiesStrategy) {
             case  AVERAGE:  // Replace ranks with average
                 fill(ranks, tiesTrace, (2 * c + length - 1) / 2d);
@@ -344,7 +344,7 @@
                 Iterator<Integer> iterator = tiesTrace.iterator();
                 long f = Math.round(c);
                 while (iterator.hasNext()) {
-                    ranks[iterator.next()] = 
+                    ranks[iterator.next()] =
                         randomData.nextLong(f, f + length - 1);
                 }
                 break;
@@ -359,12 +359,12 @@
                 break;
             default: // this should not happen unless TiesStrategy enum is changed
                 throw MathRuntimeException.createInternalError(null);
-        }   
+        }
     }
-    
+
     /**
      * Sets<code>data[i] = value</code> for each i in <code>tiesTrace.</code>
-     * 
+     *
      * @param data array to modify
      * @param tiesTrace list of index values to set
      * @param value value to set
@@ -375,10 +375,10 @@
             data[iterator.next()] = value;
         }
     }
-    
+
     /**
      * Set <code>ranks[i] = Double.NaN</code> for each i in <code>nanPositions.</code>
-     * 
+     *
      * @param ranks array to modify
      * @param nanPositions list of index values to set to <code>Double.NaN</code>
      */
@@ -388,14 +388,14 @@
         }
         Iterator<Integer> iterator = nanPositions.iterator();
         while (iterator.hasNext()) {
-            ranks[iterator.next().intValue()] = Double.NaN;  
+            ranks[iterator.next().intValue()] = Double.NaN;
         }
-        
+
     }
-    
+
     /**
      * Returns a list of indexes where <code>ranks</code> is <code>NaN.</code>
-     * 
+     *
      * @param ranks array to search for <code>NaNs</code>
      * @return list of indexes i such that <code>ranks[i] = NaN</code>
      */
@@ -406,9 +406,9 @@
                 out.add(Integer.valueOf(i));
             }
         }
-        return out;     
+        return out;
     }
-    
+
     /**
      * Represents the position of a double value in an ordering.
      * Comparable interface is implemented so Arrays.sort can be used
@@ -436,7 +436,7 @@
         /**
          * Compare this IntDoublePair to another pair.
          * Only the <strong>values</strong> are compared.
-         * 
+         *
          * @param other the other pair to compare this to
          * @return result of <code>Double.compare(value, other.value)</code>
          */



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