source: trunk/sources/ALGLIB/correlationtests.cs @ 2575

/*************************************************************************
Copyright (c) 2007, Sergey Bochkanov (ALGLIB project).

>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the 
License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses

>>> END OF LICENSE >>>
*************************************************************************/

using System;

namespace alglib
{
    public class correlationtests
    {
        /*************************************************************************
        Pearson's correlation coefficient significance test

        This test checks hypotheses about whether X  and  Y  are  samples  of  two
        continuous  distributions  having  zero  correlation  or   whether   their
        correlation is non-zero.

        The following tests are performed:
            * two-tailed test (null hypothesis - X and Y have zero correlation)
            * left-tailed test (null hypothesis - the correlation  coefficient  is
              greater than or equal to 0)
            * right-tailed test (null hypothesis - the correlation coefficient  is
              less than or equal to 0).

        Requirements:
            * the number of elements in each sample is not less than 5
            * normality of distributions of X and Y.

        Input parameters:
            R   -   Pearson's correlation coefficient for X and Y
            N   -   number of elements in samples, N>=5.

        Output parameters:
            BothTails   -   p-value for two-tailed test.
                            If BothTails is less than the given significance level
                            the null hypothesis is rejected.
            LeftTail    -   p-value for left-tailed test.
                            If LeftTail is less than the given significance level,
                            the null hypothesis is rejected.
            RightTail   -   p-value for right-tailed test.
                            If RightTail is less than the given significance level
                            the null hypothesis is rejected.

          -- ALGLIB --
             Copyright 09.04.2007 by Bochkanov Sergey
        *************************************************************************/
        public static void pearsoncorrelationsignificance(double r,
            int n,
            ref double bothtails,
            ref double lefttail,
            ref double righttail)
        {
            double t = 0;
            double p = 0;

            
            //
            // Some special cases
            //
            if( (double)(r)>=(double)(1) )
            {
                bothtails = 0.0;
                lefttail = 1.0;
                righttail = 0.0;
                return;
            }
            if( (double)(r)<=(double)(-1) )
            {
                bothtails = 0.0;
                lefttail = 0.0;
                righttail = 1.0;
                return;
            }
            if( n<5 )
            {
                bothtails = 1.0;
                lefttail = 1.0;
                righttail = 1.0;
                return;
            }
            
            //
            // General case
            //
            t = r*Math.Sqrt((n-2)/(1-AP.Math.Sqr(r)));
            p = studenttdistr.studenttdistribution(n-2, t);
            bothtails = 2*Math.Min(p, 1-p);
            lefttail = p;
            righttail = 1-p;
        }


        /*************************************************************************
        Spearman's rank correlation coefficient significance test

        This test checks hypotheses about whether X  and  Y  are  samples  of  two
        continuous  distributions  having  zero  correlation  or   whether   their
        correlation is non-zero.

        The following tests are performed:
            * two-tailed test (null hypothesis - X and Y have zero correlation)
            * left-tailed test (null hypothesis - the correlation  coefficient  is
              greater than or equal to 0)
            * right-tailed test (null hypothesis - the correlation coefficient  is
              less than or equal to 0).

        Requirements:
            * the number of elements in each sample is not less than 5.

        The test is non-parametric and doesn't require distributions X and Y to be
        normal.

        Input parameters:
            R   -   Spearman's rank correlation coefficient for X and Y
            N   -   number of elements in samples, N>=5.

        Output parameters:
            BothTails   -   p-value for two-tailed test.
                            If BothTails is less than the given significance level
                            the null hypothesis is rejected.
            LeftTail    -   p-value for left-tailed test.
                            If LeftTail is less than the given significance level,
                            the null hypothesis is rejected.
            RightTail   -   p-value for right-tailed test.
                            If RightTail is less than the given significance level
                            the null hypothesis is rejected.

          -- ALGLIB --
             Copyright 09.04.2007 by Bochkanov Sergey
        *************************************************************************/
        public static void spearmanrankcorrelationsignificance(double r,
            int n,
            ref double bothtails,
            ref double lefttail,
            ref double righttail)
        {
            double t = 0;
            double p = 0;

            
            //
            // Special case
            //
            if( n<5 )
            {
                bothtails = 1.0;
                lefttail = 1.0;
                righttail = 1.0;
                return;
            }
            
            //
            // General case
            //
            if( (double)(r)>=(double)(1) )
            {
                t = 1.0E10;
            }
            else
            {
                if( (double)(r)<=(double)(-1) )
                {
                    t = -1.0E10;
                }
                else
                {
                    t = r*Math.Sqrt((n-2)/(1-AP.Math.Sqr(r)));
                }
            }
            if( (double)(t)<(double)(0) )
            {
                p = spearmantail(t, n);
                bothtails = 2*p;
                lefttail = p;
                righttail = 1-p;
            }
            else
            {
                p = spearmantail(-t, n);
                bothtails = 2*p;
                lefttail = 1-p;
                righttail = p;
            }
        }


        /*************************************************************************
        Tail(S, 5)
        *************************************************************************/
        private static double spearmantail5(double s)
        {
            double result = 0;

            if( (double)(s)<(double)(0.000e+00) )
            {
                result = studenttdistr.studenttdistribution(3, -s);
                return result;
            }
            if( (double)(s)>=(double)(3.580e+00) )
            {
                result = 8.304e-03;
                return result;
            }
            if( (double)(s)>=(double)(2.322e+00) )
            {
                result = 4.163e-02;
                return result;
            }
            if( (double)(s)>=(double)(1.704e+00) )
            {
                result = 6.641e-02;
                return result;
            }
            if( (double)(s)>=(double)(1.303e+00) )
            {
                result = 1.164e-01;
                return result;
            }
            if( (double)(s)>=(double)(1.003e+00) )
            {
                result = 1.748e-01;
                return result;
            }
            if( (double)(s)>=(double)(7.584e-01) )
            {
                result = 2.249e-01;
                return result;
            }
            if( (double)(s)>=(double)(5.468e-01) )
            {
                result = 2.581e-01;
                return result;
            }
            if( (double)(s)>=(double)(3.555e-01) )
            {
                result = 3.413e-01;
                return result;
            }
            if( (double)(s)>=(double)(1.759e-01) )
            {
                result = 3.911e-01;
                return result;
            }
            if( (double)(s)>=(double)(1.741e-03) )
            {
                result = 4.747e-01;
                return result;
            }
            if( (double)(s)>=(double)(0.000e+00) )
            {
                result = 5.248e-01;
                return result;
            }
            result = 0;
            return result;
        }


        /*************************************************************************
        Tail(S, 6)
        *************************************************************************/
        private static double spearmantail6(double s)
        {
            double result = 0;

            if( (double)(s)<(double)(1.001e+00) )
            {
                result = studenttdistr.studenttdistribution(4, -s);
                return result;
            }
            if( (double)(s)>=(double)(5.663e+00) )
            {
                result = 1.366e-03;
                return result;
            }
            if( (double)(s)>=(double)(3.834e+00) )
            {
                result = 8.350e-03;
                return result;
            }
            if( (double)(s)>=(double)(2.968e+00) )
            {
                result = 1.668e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.430e+00) )
            {
                result = 2.921e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.045e+00) )
            {
                result = 5.144e-02;
                return result;
            }
            if( (double)(s)>=(double)(1.747e+00) )
            {
                result = 6.797e-02;
                return result;
            }
            if( (double)(s)>=(double)(1.502e+00) )
            {
                result = 8.752e-02;
                return result;
            }
            if( (double)(s)>=(double)(1.295e+00) )
            {
                result = 1.210e-01;
                return result;
            }
            if( (double)(s)>=(double)(1.113e+00) )
            {
                result = 1.487e-01;
                return result;
            }
            if( (double)(s)>=(double)(1.001e+00) )
            {
                result = 1.780e-01;
                return result;
            }
            result = 0;
            return result;
        }


        /*************************************************************************
        Tail(S, 7)
        *************************************************************************/
        private static double spearmantail7(double s)
        {
            double result = 0;

            if( (double)(s)<(double)(1.001e+00) )
            {
                result = studenttdistr.studenttdistribution(5, -s);
                return result;
            }
            if( (double)(s)>=(double)(8.159e+00) )
            {
                result = 2.081e-04;
                return result;
            }
            if( (double)(s)>=(double)(5.620e+00) )
            {
                result = 1.393e-03;
                return result;
            }
            if( (double)(s)>=(double)(4.445e+00) )
            {
                result = 3.398e-03;
                return result;
            }
            if( (double)(s)>=(double)(3.728e+00) )
            {
                result = 6.187e-03;
                return result;
            }
            if( (double)(s)>=(double)(3.226e+00) )
            {
                result = 1.200e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.844e+00) )
            {
                result = 1.712e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.539e+00) )
            {
                result = 2.408e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.285e+00) )
            {
                result = 3.320e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.068e+00) )
            {
                result = 4.406e-02;
                return result;
            }
            if( (double)(s)>=(double)(1.879e+00) )
            {
                result = 5.478e-02;
                return result;
            }
            if( (double)(s)>=(double)(1.710e+00) )
            {
                result = 6.946e-02;
                return result;
            }
            if( (double)(s)>=(double)(1.559e+00) )
            {
                result = 8.331e-02;
                return result;
            }
            if( (double)(s)>=(double)(1.420e+00) )
            {
                result = 1.001e-01;
                return result;
            }
            if( (double)(s)>=(double)(1.292e+00) )
            {
                result = 1.180e-01;
                return result;
            }
            if( (double)(s)>=(double)(1.173e+00) )
            {
                result = 1.335e-01;
                return result;
            }
            if( (double)(s)>=(double)(1.062e+00) )
            {
                result = 1.513e-01;
                return result;
            }
            if( (double)(s)>=(double)(1.001e+00) )
            {
                result = 1.770e-01;
                return result;
            }
            result = 0;
            return result;
        }


        /*************************************************************************
        Tail(S, 8)
        *************************************************************************/
        private static double spearmantail8(double s)
        {
            double result = 0;

            if( (double)(s)<(double)(2.001e+00) )
            {
                result = studenttdistr.studenttdistribution(6, -s);
                return result;
            }
            if( (double)(s)>=(double)(1.103e+01) )
            {
                result = 2.194e-05;
                return result;
            }
            if( (double)(s)>=(double)(7.685e+00) )
            {
                result = 2.008e-04;
                return result;
            }
            if( (double)(s)>=(double)(6.143e+00) )
            {
                result = 5.686e-04;
                return result;
            }
            if( (double)(s)>=(double)(5.213e+00) )
            {
                result = 1.138e-03;
                return result;
            }
            if( (double)(s)>=(double)(4.567e+00) )
            {
                result = 2.310e-03;
                return result;
            }
            if( (double)(s)>=(double)(4.081e+00) )
            {
                result = 3.634e-03;
                return result;
            }
            if( (double)(s)>=(double)(3.697e+00) )
            {
                result = 5.369e-03;
                return result;
            }
            if( (double)(s)>=(double)(3.381e+00) )
            {
                result = 7.708e-03;
                return result;
            }
            if( (double)(s)>=(double)(3.114e+00) )
            {
                result = 1.087e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.884e+00) )
            {
                result = 1.397e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.682e+00) )
            {
                result = 1.838e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.502e+00) )
            {
                result = 2.288e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.340e+00) )
            {
                result = 2.883e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.192e+00) )
            {
                result = 3.469e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.057e+00) )
            {
                result = 4.144e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.001e+00) )
            {
                result = 4.804e-02;
                return result;
            }
            result = 0;
            return result;
        }


        /*************************************************************************
        Tail(S, 9)
        *************************************************************************/
        private static double spearmantail9(double s)
        {
            double result = 0;

            if( (double)(s)<(double)(2.001e+00) )
            {
                result = studenttdistr.studenttdistribution(7, -s);
                return result;
            }
            if( (double)(s)>=(double)(9.989e+00) )
            {
                result = 2.306e-05;
                return result;
            }
            if( (double)(s)>=(double)(8.069e+00) )
            {
                result = 8.167e-05;
                return result;
            }
            if( (double)(s)>=(double)(6.890e+00) )
            {
                result = 1.744e-04;
                return result;
            }
            if( (double)(s)>=(double)(6.077e+00) )
            {
                result = 3.625e-04;
                return result;
            }
            if( (double)(s)>=(double)(5.469e+00) )
            {
                result = 6.450e-04;
                return result;
            }
            if( (double)(s)>=(double)(4.991e+00) )
            {
                result = 1.001e-03;
                return result;
            }
            if( (double)(s)>=(double)(4.600e+00) )
            {
                result = 1.514e-03;
                return result;
            }
            if( (double)(s)>=(double)(4.272e+00) )
            {
                result = 2.213e-03;
                return result;
            }
            if( (double)(s)>=(double)(3.991e+00) )
            {
                result = 2.990e-03;
                return result;
            }
            if( (double)(s)>=(double)(3.746e+00) )
            {
                result = 4.101e-03;
                return result;
            }
            if( (double)(s)>=(double)(3.530e+00) )
            {
                result = 5.355e-03;
                return result;
            }
            if( (double)(s)>=(double)(3.336e+00) )
            {
                result = 6.887e-03;
                return result;
            }
            if( (double)(s)>=(double)(3.161e+00) )
            {
                result = 8.598e-03;
                return result;
            }
            if( (double)(s)>=(double)(3.002e+00) )
            {
                result = 1.065e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.855e+00) )
            {
                result = 1.268e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.720e+00) )
            {
                result = 1.552e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.595e+00) )
            {
                result = 1.836e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.477e+00) )
            {
                result = 2.158e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.368e+00) )
            {
                result = 2.512e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.264e+00) )
            {
                result = 2.942e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.166e+00) )
            {
                result = 3.325e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.073e+00) )
            {
                result = 3.800e-02;
                return result;
            }
            if( (double)(s)>=(double)(2.001e+00) )
            {
                result = 4.285e-02;
                return result;
            }
            result = 0;
            return result;
        }


        /*************************************************************************
        Tail(T,N), accepts T<0
        *************************************************************************/
        private static double spearmantail(double t,
            int n)
        {
            double result = 0;

            if( n==5 )
            {
                result = spearmantail5(-t);
                return result;
            }
            if( n==6 )
            {
                result = spearmantail6(-t);
                return result;
            }
            if( n==7 )
            {
                result = spearmantail7(-t);
                return result;
            }
            if( n==8 )
            {
                result = spearmantail8(-t);
                return result;
            }
            if( n==9 )
            {
                result = spearmantail9(-t);
                return result;
            }
            result = studenttdistr.studenttdistribution(n-2, t);
            return result;
        }
    }
}