ttestimpl.java

Apache的common math数学软件包

     *
     * @param mu constant value to compare sample mean against
     * @param sampleStats StatisticalSummary describing sample data values
     * @param alpha significance level of the test
     * @return p-value
     * @throws IllegalArgumentException if the precondition is not met
     * @throws MathException if an error occurs computing the p-value
     */
    public boolean tTest( double mu, StatisticalSummary sampleStats,
            double alpha)
    throws IllegalArgumentException, MathException {
        if ((alpha <= 0) || (alpha > 0.5)) {
            throw new IllegalArgumentException("bad significance level: " + alpha);
        }
        return (tTest(mu, sampleStats) < alpha);
    }

    /**
     * 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. 
     * 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 
     * 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 
     * <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 
     * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
     * here</a></p>
     * <p>
     * <strong>Preconditions</strong>: <ul>
     * <li>The observed array lengths must both be at least 2.
     * </li></ul></p>
     *
     * @param sample1 array of sample data values
     * @param sample2 array of sample data values
     * @return p-value for t-test
     * @throws IllegalArgumentException if the precondition is not met
     * @throws MathException if an error occurs computing the p-value
     */
    public double tTest(double[] sample1, double[] sample2)
    throws IllegalArgumentException, MathException {
        if ((sample1 == null) || (sample2 == null ||
                Math.min(sample1.length, sample2.length) < 2)) {
            throw new IllegalArgumentException("insufficient data");
        }
        return tTest(StatUtils.mean(sample1), StatUtils.mean(sample2),
                StatUtils.variance(sample1), StatUtils.variance(sample2),
                (double) sample1.length, (double) sample2.length);
    }
    
    /**
     * 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
     * {@link #tTest(double[], double[])}.
     * <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. 
     * 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
     * {@link #homoscedasticT(double[], double[])}. The sum of the sample sizes
     * minus 2 is used as the degrees of freedom.</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 
     * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
     * here</a></p>
     * <p>
     * <strong>Preconditions</strong>: <ul>
     * <li>The observed array lengths must both be at least 2.
     * </li></ul></p>
     *
     * @param sample1 array of sample data values
     * @param sample2 array of sample data values
     * @return p-value for t-test
     * @throws IllegalArgumentException if the precondition is not met
     * @throws MathException if an error occurs computing the p-value
     */
    public double homoscedasticTTest(double[] sample1, double[] sample2)
    throws IllegalArgumentException, MathException {
        if ((sample1 == null) || (sample2 == null ||
                Math.min(sample1.length, sample2.length) < 2)) {
            throw new IllegalArgumentException("insufficient data");
        }
        return homoscedasticTTest(StatUtils.mean(sample1), 
                StatUtils.mean(sample2), StatUtils.variance(sample1),
                StatUtils.variance(sample2), (double) sample1.length, 
                (double) sample2.length);
    }
    

     /**
     * 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, 
     * 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 
     * {@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 
     * 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 
     * <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 
     * <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 
     * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
     * here</a></p>
     * <p>
     * <strong>Preconditions</strong>: <ul>
     * <li>The observed array lengths must both be at least 2.
     * </li>
     * <li> <code> 0 < alpha < 0.5 </code>
     * </li></ul></p>
     *
     * @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 
     * confidence 1 - alpha
     * @throws IllegalArgumentException if the preconditions are not met
     * @throws MathException if an error occurs performing the test
     */
    public boolean tTest(double[] sample1, double[] sample2,
            double alpha)
    throws IllegalArgumentException, MathException {
        if ((alpha <= 0) || (alpha > 0.5)) {
            throw new IllegalArgumentException("bad significance level: " + alpha);
        }
        return (tTest(sample1, sample2) < alpha);
    }
    
    /**
     * 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, 
     * with significance level <code>alpha</code>,  assuming that the
     * 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 
     * perform a 1-sided test, use <code>alpha * 2.</code>  To perform the test
     * 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
     * {@link #t(double[], double[])} for the formula. The sum of the sample
     * sizes minus 2 is used as the degrees of freedom.</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 <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
     * <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 
     * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
     * here</a></p>
     * <p>
     * <strong>Preconditions</strong>: <ul>
     * <li>The observed array lengths must both be at least 2.
     * </li>
     * <li> <code> 0 < alpha < 0.5 </code>
     * </li></ul></p>
     *
     * @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 
     * confidence 1 - alpha
     * @throws IllegalArgumentException if the preconditions are not met
     * @throws MathException if an error occurs performing the test
     */
    public boolean homoscedasticTTest(double[] sample1, double[] sample2,
            double alpha)
    throws IllegalArgumentException, MathException {
        if ((alpha <= 0) || (alpha > 0.5)) {
            throw new IllegalArgumentException("bad significance level: " + alpha);
        }
        return (homoscedasticTTest(sample1, sample2) < alpha);
    }

     /**
     * 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. 
     * 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 
     * sample data to compute the p-value.   To perform the test assuming
     * 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 
     * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">
     * here</a></p>
     * <p>
     * <strong>Preconditions</strong>: <ul>
     * <li>The datasets described by the two Univariates must each contain
     * at least 2 observations.
     * </li></ul></p>
     *
     * @param sampleStats1  StatisticalSummary describing data from the first sample
     * @param sampleStats2  StatisticalSummary describing data from the second sample
     * @return p-value for t-test
     * @throws IllegalArgumentException if the precondition is not met
     * @throws MathException if an error occurs computing the p-value
     */
    public double tTest(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2)
    throws IllegalArgumentException, MathException {
        if ((sampleStats1 == null) || (sampleStats2 == null ||
                Math.min(sampleStats1.getN(), sampleStats2.getN()) < 2)) {