org.apache.commons.math.distribution.TDistributionImpl Java Examples
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org.apache.commons.math.distribution.TDistributionImpl.
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Example #1
Source File: PearsonsCorrelationTest.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); } } }
Example #2
Source File: PearsonsCorrelationTest.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); } } }
Example #3
Source File: Math_69_PearsonsCorrelation_t.java From coming with MIT License | 6 votes |
/** * 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 * tDistribution.cumulativeProbability(-t); } } } return new BlockRealMatrix(out); }
Example #4
Source File: SimpleRegression.java From astor with GNU General Public License v2.0 | 6 votes |
/** * Removes the observation (x,y) from the regression data set. * <p> * Mirrors the addData method. This method permits the use of * SimpleRegression instances in streaming mode where the regression * is applied to a sliding "window" of observations, however the caller is * responsible for maintaining the set of observations in the window.</p> * * The method has no effect if there are no points of data (i.e. n=0) * * @param x independent variable value * @param y dependent variable value */ public void removeData(double x, double y) { if (n > 0) { double dx = x - xbar; double dy = y - ybar; sumXX -= dx * dx * (double) n / (n - 1d); sumYY -= dy * dy * (double) n / (n - 1d); sumXY -= dx * dy * (double) n / (n - 1d); xbar -= dx / (n - 1.0); ybar -= dy / (n - 1.0); sumX -= x; sumY -= y; n--; if (n > 2) { distribution = new TDistributionImpl(n - 2); } } }
Example #5
Source File: Math_69_PearsonsCorrelation_s.java From coming with MIT License | 6 votes |
/** * 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); }
Example #6
Source File: Nopol2017_0076_s.java From coming with MIT License | 6 votes |
/** * 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); }
Example #7
Source File: PearsonsCorrelationTest.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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 = FastMath.abs(rValues.getEntry(i, j)) / stdErrors.getEntry(i, j); double p = 2 * (1 - tDistribution.cumulativeProbability(t)); assertEquals(p, pValues.getEntry(i, j), 10E-15); } } }
Example #8
Source File: PearsonsCorrelation.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); }
Example #9
Source File: SimpleRegression.java From astor with GNU General Public License v2.0 | 6 votes |
/** * Adds the observation (x,y) to the regression data set. * <p> * Uses updating formulas for means and sums of squares defined in * "Algorithms for Computing the Sample Variance: Analysis and * Recommendations", Chan, T.F., Golub, G.H., and LeVeque, R.J. * 1983, American Statistician, vol. 37, pp. 242-247, referenced in * Weisberg, S. "Applied Linear Regression". 2nd Ed. 1985.</p> * * * @param x independent variable value * @param y dependent variable value */ public void addData(double x, double y) { if (n == 0) { xbar = x; ybar = y; } else { double dx = x - xbar; double dy = y - ybar; sumXX += dx * dx * (double) n / (n + 1d); sumYY += dy * dy * (double) n / (n + 1d); sumXY += dx * dy * (double) n / (n + 1d); xbar += dx / (n + 1.0); ybar += dy / (n + 1.0); } sumX += x; sumY += y; n++; if (n > 2) { distribution = new TDistributionImpl(n - 2); } }
Example #10
Source File: SimpleRegression.java From astor with GNU General Public License v2.0 | 6 votes |
/** * Removes the observation (x,y) from the regression data set. * <p> * Mirrors the addData method. This method permits the use of * SimpleRegression instances in streaming mode where the regression * is applied to a sliding "window" of observations, however the caller is * responsible for maintaining the set of observations in the window.</p> * * The method has no effect if there are no points of data (i.e. n=0) * * @param x independent variable value * @param y dependent variable value */ public void removeData(double x, double y) { if (n > 0) { double dx = x - xbar; double dy = y - ybar; sumXX -= dx * dx * (double) n / (n - 1d); sumYY -= dy * dy * (double) n / (n - 1d); sumXY -= dx * dy * (double) n / (n - 1d); xbar -= dx / (n - 1.0); ybar -= dy / (n - 1.0); sumX -= x; sumY -= y; n--; if (n > 2) { distribution = new TDistributionImpl(n - 2); } } }
Example #11
Source File: PearsonsCorrelationTest.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); } } }
Example #12
Source File: PearsonsCorrelationTest.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); } } }
Example #13
Source File: PearsonsCorrelation.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); }
Example #14
Source File: PearsonsCorrelationTest.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); } } }
Example #15
Source File: PearsonsCorrelation.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); }
Example #16
Source File: PearsonsCorrelationTest.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); } } }
Example #17
Source File: PearsonsCorrelation.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); }
Example #18
Source File: PearsonsCorrelation.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); }
Example #19
Source File: PearsonsCorrelationTest.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); } } }
Example #20
Source File: PearsonsCorrelationTest.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); } } }
Example #21
Source File: PearsonsCorrelation.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); }
Example #22
Source File: PearsonsCorrelationTest.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); } } }
Example #23
Source File: PearsonsCorrelation.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); }
Example #24
Source File: PearsonsCorrelationTest.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); } } }
Example #25
Source File: SimpleRegression.java From astor with GNU General Public License v2.0 | 6 votes |
/** * Adds the observation (x,y) to the regression data set. * <p> * Uses updating formulas for means and sums of squares defined in * "Algorithms for Computing the Sample Variance: Analysis and * Recommendations", Chan, T.F., Golub, G.H., and LeVeque, R.J. * 1983, American Statistician, vol. 37, pp. 242-247, referenced in * Weisberg, S. "Applied Linear Regression". 2nd Ed. 1985.</p> * * * @param x independent variable value * @param y dependent variable value */ public void addData(double x, double y) { if (n == 0) { xbar = x; ybar = y; } else { double dx = x - xbar; double dy = y - ybar; sumXX += dx * dx * (double) n / (n + 1d); sumYY += dy * dy * (double) n / (n + 1d); sumXY += dx * dy * (double) n / (n + 1d); xbar += dx / (n + 1.0); ybar += dy / (n + 1.0); } sumX += x; sumY += y; n++; if (n > 2) { distribution = new TDistributionImpl(n - 2); } }
Example #26
Source File: SimpleRegression.java From astor with GNU General Public License v2.0 | 6 votes |
/** * Removes the observation (x,y) from the regression data set. * <p> * Mirrors the addData method. This method permits the use of * SimpleRegression instances in streaming mode where the regression * is applied to a sliding "window" of observations, however the caller is * responsible for maintaining the set of observations in the window.</p> * * The method has no effect if there are no points of data (i.e. n=0) * * @param x independent variable value * @param y dependent variable value */ public void removeData(double x, double y) { if (n > 0) { double dx = x - xbar; double dy = y - ybar; sumXX -= dx * dx * (double) n / (n - 1d); sumYY -= dy * dy * (double) n / (n - 1d); sumXY -= dx * dy * (double) n / (n - 1d); xbar -= dx / (n - 1.0); ybar -= dy / (n - 1.0); sumX -= x; sumY -= y; n--; if (n > 2) { distribution = new TDistributionImpl(n - 2); } } }
Example #27
Source File: PearsonsCorrelationTest.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); } } }
Example #28
Source File: PearsonsCorrelation.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); }
Example #29
Source File: PearsonsCorrelationTest.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); } } }
Example #30
Source File: PearsonsCorrelationTest.java From astor with GNU General Public License v2.0 | 6 votes |
/** * 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); } } }