Java Code Examples for org.apache.commons.math.distribution.TDistribution#cumulativeProbability()

/**
 * Returns a matrix of p-values associated with the (two-sided) null
 * hypothesis that the corresponding correlation coefficient is zero.
 * <p><code>getCorrelationPValues().getEntry(i,j)</code> is the probability
 * that a random variable distributed as <code>t<sub>n-2</sub></code> takes
 * a value with absolute value greater than or equal to <br>
 * <code>|r|((n - 2) / (1 - r<sup>2</sup>))<sup>1/2</sup></code></p>
 * <p>The values in the matrix are sometimes referred to as the 
 * <i>significance</i> of the corresponding correlation coefficients.</p>
 * 
 * @return matrix of p-values
 * @throws MathException if an error occurs estimating probabilities
 */
public RealMatrix getCorrelationPValues() throws MathException {
    TDistribution tDistribution = new TDistributionImpl(nObs - 2);
    int nVars = correlationMatrix.getColumnDimension();
    double[][] out = new double[nVars][nVars];
    for (int i = 0; i < nVars; i++) {
        for (int j = 0; j < nVars; j++) {
            if (i == j) {
                out[i][j] = 0d;
            } else {
                double r = correlationMatrix.getEntry(i, j);
                double t = Math.abs(r * Math.sqrt((nObs - 2)/(1 - r * r)));
                out[i][j] = 2 * (1 - tDistribution.cumulativeProbability(t));
            }
        }
    }
    return new BlockRealMatrix(out);
}
 

/**
 * Verify that direct t-tests using standard error estimates are consistent
 * with reported p-values
 */
public void testStdErrorConsistency() throws Exception {
    TDistribution tDistribution = new TDistributionImpl(45);
    RealMatrix matrix = createRealMatrix(swissData, 47, 5);
    PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
    RealMatrix rValues = corrInstance.getCorrelationMatrix();
    RealMatrix pValues = corrInstance.getCorrelationPValues();
    RealMatrix stdErrors = corrInstance.getCorrelationStandardErrors();
    for (int i = 0; i < 5; i++) {
        for (int j = 0; j < i; j++) {
            double t = Math.abs(rValues.getEntry(i, j)) / stdErrors.getEntry(i, j);
            double p = 2 * (1 - tDistribution.cumulativeProbability(t));
            assertEquals(p, pValues.getEntry(i, j), 10E-15);
        }
    }
}
 

/**
 * Verify that direct t-tests using standard error estimates are consistent
 * with reported p-values
 */
@Test
public void testStdErrorConsistency() throws Exception {
    TDistribution tDistribution = new TDistributionImpl(45);
    RealMatrix matrix = createRealMatrix(swissData, 47, 5);
    PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
    RealMatrix rValues = corrInstance.getCorrelationMatrix();
    RealMatrix pValues = corrInstance.getCorrelationPValues();
    RealMatrix stdErrors = corrInstance.getCorrelationStandardErrors();
    for (int i = 0; i < 5; i++) {
        for (int j = 0; j < i; j++) {
            double t = FastMath.abs(rValues.getEntry(i, j)) / stdErrors.getEntry(i, j);
            double p = 2 * (1 - tDistribution.cumulativeProbability(t));
            Assert.assertEquals(p, pValues.getEntry(i, j), 10E-15);
        }
    }
}
 

/**
 * Returns a matrix of p-values associated with the (two-sided) null
 * hypothesis that the corresponding correlation coefficient is zero.
 * <p><code>getCorrelationPValues().getEntry(i,j)</code> is the probability
 * that a random variable distributed as <code>t<sub>n-2</sub></code> takes
 * a value with absolute value greater than or equal to <br>
 * <code>|r|((n - 2) / (1 - r<sup>2</sup>))<sup>1/2</sup></code></p>
 * <p>The values in the matrix are sometimes referred to as the
 * <i>significance</i> of the corresponding correlation coefficients.</p>
 *
 * @return matrix of p-values
 * @throws MathException if an error occurs estimating probabilities
 */
public RealMatrix getCorrelationPValues() throws MathException {
    TDistribution tDistribution = new TDistributionImpl(nObs - 2);
    int nVars = correlationMatrix.getColumnDimension();
    double[][] out = new double[nVars][nVars];
    for (int i = 0; i < nVars; i++) {
        for (int j = 0; j < nVars; j++) {
            if (i == j) {
                out[i][j] = 0d;
            } else {
                double r = correlationMatrix.getEntry(i, j);
                double t = FastMath.abs(r * FastMath.sqrt((nObs - 2)/(1 - r * r)));
                out[i][j] = 2 * tDistribution.cumulativeProbability(-t);
            }
        }
    }
    return new BlockRealMatrix(out);
}
 

/**
 * Returns a matrix of p-values associated with the (two-sided) null
 * hypothesis that the corresponding correlation coefficient is zero.
 * <p><code>getCorrelationPValues().getEntry(i,j)</code> is the probability
 * that a random variable distributed as <code>t<sub>n-2</sub></code> takes
 * a value with absolute value greater than or equal to <br>
 * <code>|r|((n - 2) / (1 - r<sup>2</sup>))<sup>1/2</sup></code></p>
 * <p>The values in the matrix are sometimes referred to as the
 * <i>significance</i> of the corresponding correlation coefficients.</p>
 *
 * @return matrix of p-values
 * @throws MathException if an error occurs estimating probabilities
 */
public RealMatrix getCorrelationPValues() throws MathException {
    TDistribution tDistribution = new TDistributionImpl(nObs - 2);
    int nVars = correlationMatrix.getColumnDimension();
    double[][] out = new double[nVars][nVars];
    for (int i = 0; i < nVars; i++) {
        for (int j = 0; j < nVars; j++) {
            if (i == j) {
                out[i][j] = 0d;
            } else {
                double r = correlationMatrix.getEntry(i, j);
                double t = FastMath.abs(r * FastMath.sqrt((nObs - 2)/(1 - r * r)));
                out[i][j] = 2 * tDistribution.cumulativeProbability(-t);
            }
        }
    }
    return new BlockRealMatrix(out);
}
 

/**
 * Returns a matrix of p-values associated with the (two-sided) null
 * hypothesis that the corresponding correlation coefficient is zero.
 * <p><code>getCorrelationPValues().getEntry(i,j)</code> is the probability
 * that a random variable distributed as <code>t<sub>n-2</sub></code> takes
 * a value with absolute value greater than or equal to <br>
 * <code>|r|((n - 2) / (1 - r<sup>2</sup>))<sup>1/2</sup></code></p>
 * <p>The values in the matrix are sometimes referred to as the
 * <i>significance</i> of the corresponding correlation coefficients.</p>
 *
 * @return matrix of p-values
 * @throws MathException if an error occurs estimating probabilities
 */
public RealMatrix getCorrelationPValues() throws MathException {
    TDistribution tDistribution = new TDistributionImpl(nObs - 2);
    int nVars = correlationMatrix.getColumnDimension();
    double[][] out = new double[nVars][nVars];
    for (int i = 0; i < nVars; i++) {
        for (int j = 0; j < nVars; j++) {
            if (i == j) {
                out[i][j] = 0d;
            } else {
                double r = correlationMatrix.getEntry(i, j);
                double t = Math.abs(r * Math.sqrt((nObs - 2)/(1 - r * r)));
                out[i][j] = 2 * (1 - tDistribution.cumulativeProbability(t));
            }
        }
    }
    return new BlockRealMatrix(out);
}
 

/**
 * Returns a matrix of p-values associated with the (two-sided) null
 * hypothesis that the corresponding correlation coefficient is zero.
 * <p><code>getCorrelationPValues().getEntry(i,j)</code> is the probability
 * that a random variable distributed as <code>t<sub>n-2</sub></code> takes
 * a value with absolute value greater than or equal to <br>
 * <code>|r|((n - 2) / (1 - r<sup>2</sup>))<sup>1/2</sup></code></p>
 * <p>The values in the matrix are sometimes referred to as the
 * <i>significance</i> of the corresponding correlation coefficients.</p>
 *
 * @return matrix of p-values
 * @throws MathException if an error occurs estimating probabilities
 */
public RealMatrix getCorrelationPValues() throws MathException {
    TDistribution tDistribution = new TDistributionImpl(nObs - 2);
    int nVars = correlationMatrix.getColumnDimension();
    double[][] out = new double[nVars][nVars];
    for (int i = 0; i < nVars; i++) {
        for (int j = 0; j < nVars; j++) {
            if (i == j) {
                out[i][j] = 0d;
            } else {
                double r = correlationMatrix.getEntry(i, j);
                double t = Math.abs(r * Math.sqrt((nObs - 2)/(1 - r * r)));
                out[i][j] = 2 * (1 - tDistribution.cumulativeProbability(t));
            }
        }
    }
    return new BlockRealMatrix(out);
}
 

/**
 * Verify that direct t-tests using standard error estimates are consistent
 * with reported p-values
 */
public void testStdErrorConsistency() throws Exception {
    TDistribution tDistribution = new TDistributionImpl(45);
    RealMatrix matrix = createRealMatrix(swissData, 47, 5);
    PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix); 
    RealMatrix rValues = corrInstance.getCorrelationMatrix();
    RealMatrix pValues = corrInstance.getCorrelationPValues();
    RealMatrix stdErrors = corrInstance.getCorrelationStandardErrors();
    for (int i = 0; i < 5; i++) {
        for (int j = 0; j < i; j++) {
            double t = Math.abs(rValues.getEntry(i, j)) / stdErrors.getEntry(i, j);
            double p = 2 * (1 - tDistribution.cumulativeProbability(t));
            assertEquals(p, pValues.getEntry(i, j), 10E-15);
        }
    }
}
 

/**
 * Returns a matrix of p-values associated with the (two-sided) null
 * hypothesis that the corresponding correlation coefficient is zero.
 * <p><code>getCorrelationPValues().getEntry(i,j)</code> is the probability
 * that a random variable distributed as <code>t<sub>n-2</sub></code> takes
 * a value with absolute value greater than or equal to <br>
 * <code>|r|((n - 2) / (1 - r<sup>2</sup>))<sup>1/2</sup></code></p>
 * <p>The values in the matrix are sometimes referred to as the
 * <i>significance</i> of the corresponding correlation coefficients.</p>
 *
 * @return matrix of p-values
 * @throws MathException if an error occurs estimating probabilities
 */
public RealMatrix getCorrelationPValues() throws MathException {
    TDistribution tDistribution = new TDistributionImpl(nObs - 2);
    int nVars = correlationMatrix.getColumnDimension();
    double[][] out = new double[nVars][nVars];
    for (int i = 0; i < nVars; i++) {
        for (int j = 0; j < nVars; j++) {
            if (i == j) {
                out[i][j] = 0d;
            } else {
                double r = correlationMatrix.getEntry(i, j);
                double t = Math.abs(r * Math.sqrt((nObs - 2)/(1 - r * r)));
                out[i][j] = 2 * (1 - tDistribution.cumulativeProbability(t));
            }
        }
    }
    return new BlockRealMatrix(out);
}
 

/**
 * Verify that direct t-tests using standard error estimates are consistent
 * with reported p-values
 */
public void testStdErrorConsistency() throws Exception {
    TDistribution tDistribution = new TDistributionImpl(45);
    RealMatrix matrix = createRealMatrix(swissData, 47, 5);
    PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
    RealMatrix rValues = corrInstance.getCorrelationMatrix();
    RealMatrix pValues = corrInstance.getCorrelationPValues();
    RealMatrix stdErrors = corrInstance.getCorrelationStandardErrors();
    for (int i = 0; i < 5; i++) {
        for (int j = 0; j < i; j++) {
            double t = Math.abs(rValues.getEntry(i, j)) / stdErrors.getEntry(i, j);
            double p = 2 * (1 - tDistribution.cumulativeProbability(t));
            assertEquals(p, pValues.getEntry(i, j), 10E-15);
        }
    }
}
 

/**
 * Returns a matrix of p-values associated with the (two-sided) null
 * hypothesis that the corresponding correlation coefficient is zero.
 * <p><code>getCorrelationPValues().getEntry(i,j)</code> is the probability
 * that a random variable distributed as <code>t<sub>n-2</sub></code> takes
 * a value with absolute value greater than or equal to <br>
 * <code>|r|((n - 2) / (1 - r<sup>2</sup>))<sup>1/2</sup></code></p>
 * <p>The values in the matrix are sometimes referred to as the 
 * <i>significance</i> of the corresponding correlation coefficients.</p>
 * 
 * @return matrix of p-values
 * @throws MathException if an error occurs estimating probabilities
 */
public RealMatrix getCorrelationPValues() throws MathException {
    TDistribution tDistribution = new TDistributionImpl(nObs - 2);
    int nVars = correlationMatrix.getColumnDimension();
    double[][] out = new double[nVars][nVars];
    for (int i = 0; i < nVars; i++) {
        for (int j = 0; j < nVars; j++) {
            if (i == j) {
                out[i][j] = 0d;
            } else {
                double r = correlationMatrix.getEntry(i, j);
                double t = Math.abs(r * Math.sqrt((nObs - 2)/(1 - r * r)));
                out[i][j] = 2 * (1 - tDistribution.cumulativeProbability(t));
            }
        }
    }
    return new BlockRealMatrix(out);
}
 

/**
 * Returns a matrix of p-values associated with the (two-sided) null
 * hypothesis that the corresponding correlation coefficient is zero.
 * <p><code>getCorrelationPValues().getEntry(i,j)</code> is the probability
 * that a random variable distributed as <code>t<sub>n-2</sub></code> takes
 * a value with absolute value greater than or equal to <br>
 * <code>|r|((n - 2) / (1 - r<sup>2</sup>))<sup>1/2</sup></code></p>
 * <p>The values in the matrix are sometimes referred to as the 
 * <i>significance</i> of the corresponding correlation coefficients.</p>
 * 
 * @return matrix of p-values
 * @throws MathException if an error occurs estimating probabilities
 */
public RealMatrix getCorrelationPValues() throws MathException {
    TDistribution tDistribution = new TDistributionImpl(nObs - 2);
    int nVars = correlationMatrix.getColumnDimension();
    double[][] out = new double[nVars][nVars];
    for (int i = 0; i < nVars; i++) {
        for (int j = 0; j < nVars; j++) {
            if (i == j) {
                out[i][j] = 0d;
            } else {
                double r = correlationMatrix.getEntry(i, j);
                double t = Math.abs(r * Math.sqrt((nObs - 2)/(1 - r * r)));
                out[i][j] = 2 * (1 - tDistribution.cumulativeProbability(t));
            }
        }
    }
    return new BlockRealMatrix(out);
}
 

/**
 * Computes p-value for 2-sided, 1-sample t-test.
 *
 * @param m sample mean
 * @param mu constant to test against
 * @param v sample variance
 * @param n sample n
 * @return p-value
 * @throws MathException if an error occurs computing the p-value
 */
protected double tTest(double m, double mu, double v, double n)
    throws MathException {
    double t = FastMath.abs(t(m, mu, v, n));
    TDistribution distribution = new TDistributionImpl(n - 1);
    return 2.0 * distribution.cumulativeProbability(-t);
}
 

/**
 * Computes p-value for 2-sided, 1-sample t-test.
 * 
 * @param m sample mean
 * @param mu constant to test against
 * @param v sample variance
 * @param n sample n
 * @return p-value
 * @throws MathException if an error occurs computing the p-value
 */
protected double tTest(double m, double mu, double v, double n)
throws MathException {
    double t = Math.abs(t(m, mu, v, n));
    TDistribution tDistribution = 
        getDistributionFactory().createTDistribution(n - 1);
    return 1.0 - tDistribution.cumulativeProbability(-t, t);
}
 

/**
 * Computes p-value for 2-sided, 1-sample t-test.
 *
 * @param m sample mean
 * @param mu constant to test against
 * @param v sample variance
 * @param n sample n
 * @return p-value
 * @throws MathException if an error occurs computing the p-value
 */
protected double tTest(double m, double mu, double v, double n)
    throws MathException {
    double t = FastMath.abs(t(m, mu, v, n));
    TDistribution distribution = new TDistributionImpl(n - 1);
    return 2.0 * distribution.cumulativeProbability(-t);
}
 

/**
 * Computes p-value for 2-sided, 1-sample t-test.
 *
 * @param m sample mean
 * @param mu constant to test against
 * @param v sample variance
 * @param n sample n
 * @return p-value
 * @throws MathException if an error occurs computing the p-value
 */
protected double tTest(double m, double mu, double v, double n)
    throws MathException {
    double t = FastMath.abs(t(m, mu, v, n));
    TDistribution distribution = new TDistributionImpl(n - 1);
    return 2.0 * distribution.cumulativeProbability(-t);
}
 

/**
 * Computes p-value for 2-sided, 2-sample t-test.
 * <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
 * @param v2 second sample variance
 * @param n1 first sample n
 * @param n2 second sample n
 * @return p-value
 * @throws MathException if an error occurs computing the p-value
 */
protected double tTest(double m1, double m2,
                       double v1, double v2,
                       double n1, double n2)
    throws MathException {
    double t = FastMath.abs(t(m1, m2, v1, v2, n1, n2));
    double degreesOfFreedom = 0;
    degreesOfFreedom = df(v1, v2, n1, n2);
    TDistribution distribution = new TDistributionImpl(degreesOfFreedom);
    return 2.0 * distribution.cumulativeProbability(-t);
}