/// <summary>
/// Performs a Pearson correlation test for association.
/// </summary>
/// <param name="x">The values of the first variable.</param>
/// <param name="y">The values of the second variable.</param>
/// <returns>The result of the test.</returns>
/// <remarks>
/// <para>This test measures the strength of the linear correlation between two variables. The
/// test statistic r is simply the covariance of the two variables, scaled by their respective
/// standard deviations so as to obtain a number between -1 (perfect linear anti-correlation)
/// and +1 (perfect linear correlation).</para>
/// <para>The Pearson test cannot reliably detect or rule out non-linear associations. For example,
/// variables with a perfect quadratic association may have only a weak linear correlation. If
/// you wish to test for associations that may not be linear, consider using the Spearman or
/// Kendall tests instead.</para>
/// <para>The Pearson correlation test requires O(N) operations.</para>
/// <para>The Pearson test requires at least three bivariate values.</para>
/// </remarks>
/// <exception cref="ArgumentNullException"><paramref name="x"/> or <paramref name="y"/> is <see langword="null"/>.</exception>
/// <exception cref="DimensionMismatchException"><paramref name="x"/> and <paramref name="y"/> do not contain the same number of entries.</exception>
/// <exception cref="InsufficientDataException">There are fewer than 3 entries in the sample.</exception>
/// <seealso cref="SpearmanRhoTest(IReadOnlyList{double},IReadOnlyList{double})"/>
/// <seealso cref="KendallTauTest"/>
/// <seealso href="http://en.wikipedia.org/wiki/Pearson_correlation_coefficient" />
public static TestResult PearsonRTest(IReadOnlyList <double> x, IReadOnlyList <double> y)
{
if (x == null)
{
throw new ArgumentNullException(nameof(x));
}
if (y == null)
{
throw new ArgumentNullException(nameof(y));
}
if (x.Count != y.Count)
{
throw new DimensionMismatchException();
}
int n = x.Count;
if (n < 3)
{
throw new InsufficientDataException();
}
double xMean, yMean, xxSum, yySum, xySum;
ComputeBivariateMomentsUpToTwo(x, y, out n, out xMean, out yMean, out xxSum, out yySum, out xySum);
double r = xySum / Math.Sqrt(xxSum * yySum);
ContinuousDistribution p = new PearsonRDistribution(n);
return(new TestResult("r", r, p, TestType.TwoTailed));
}
/// <summary>
/// Performs a Pearson correlation test for association.
/// </summary>
/// <returns>The result of the test.</returns>
/// <remarks>
/// <para>This test measures the strength of the linear correlation between two variables. The
/// test statistic r is simply the covariance of the two variables, scaled by their respective
/// standard deviations so as to obtain a number between -1 (perfect linear anti-correlation)
/// and +1 (perfect linear correlation).</para>
/// <para>The Pearson test cannot reliably detect or rule out non-linear associations. For example,
/// variables with a perfect quadratic association may have only a weak linear correlation. If
/// you wish to test for associations that may not be linear, consider using the Spearman or
/// Kendall tests instead.</para>
/// <para>The Pearson correlation test requires O(N) operations.</para>
/// <para>The Pearson test requires at least three bivariate values.</para>
/// </remarks>
/// <exception cref="InsufficientDataException"><see cref="Count"/> is less than three.</exception>
/// <seealso cref="SpearmanRhoTest"/>
/// <seealso cref="KendallTauTest"/>
/// <seealso href="http://en.wikipedia.org/wiki/Pearson_correlation_coefficient" />
public TestResult PearsonRTest()
{
if (Count < 3)
{
throw new InsufficientDataException();
}
double r = this.Covariance / Math.Sqrt(xData.Variance * yData.Variance);
Distribution p = new PearsonRDistribution(Count);
return(new TestResult(r, p));
}