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## Copyright (C) 1995-2015 Kurt Hornik
##
## This file is part of Octave.
##
## Octave 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; either version 3 of the License, or (at
## your option) any later version.
##
## Octave 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.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} cor_test (@var{x}, @var{y}, @var{alt}, @var{method})
## Test whether two samples @var{x} and @var{y} come from uncorrelated
## populations.
##
## The optional argument string @var{alt} describes the alternative
## hypothesis, and can be @qcode{"!="} or @qcode{"<>"} (nonzero), @qcode{">"}
## (greater than 0), or @qcode{"<"} (less than 0). The default is the
## two-sided case.
##
## The optional argument string @var{method} specifies which correlation
## coefficient to use for testing. If @var{method} is @qcode{"pearson"}
## (default), the (usual) Pearson's produt moment correlation coefficient is
## used. In this case, the data should come from a bivariate normal
## distribution. Otherwise, the other two methods offer nonparametric
## alternatives. If @var{method} is @qcode{"kendall"}, then Kendall's rank
## correlation tau is used. If @var{method} is @qcode{"spearman"}, then
## Spearman's rank correlation rho is used. Only the first character is
## necessary.
##
## The output is a structure with the following elements:
##
## @table @var
## @item pval
## The p-value of the test.
##
## @item stat
## The value of the test statistic.
##
## @item dist
## The distribution of the test statistic.
##
## @item params
## The parameters of the null distribution of the test statistic.
##
## @item alternative
## The alternative hypothesis.
##
## @item method
## The method used for testing.
## @end table
##
## If no output argument is given, the p-value is displayed.
## @end deftypefn
## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at>
## Adapted-by: KH <Kurt.Hornik@wu-wien.ac.at>
## Description: Test for zero correlation
function t = cor_test (x, y, alt, method)
if (nargin < 2 || nargin > 4)
print_usage ();
endif
if (! isvector (x) || ! isvector (y) || length (x) != length (y))
error ("cor_test: X and Y must be vectors of the same length");
endif
if (nargin < 3)
alt = "!=";
elseif (! ischar (alt))
error ("cor_test: ALT must be a string");
endif
if (nargin < 4)
method = "pearson";
elseif (! ischar (method))
error ("cor_test: METHOD must be a string");
endif
n = length (x);
m = method(1);
if (m == "p")
r = corr (x, y);
df = n - 2;
t.method = "Pearson's product moment correlation";
t.params = df;
t.stat = sqrt (df) .* r / sqrt (1 - r.^2);
t.dist = "t";
cdf = tcdf (t.stat, df);
elseif (m == "k")
tau = kendall (x, y);
t.method = "Kendall's rank correlation tau";
t.params = [];
t.stat = tau / sqrt ((2 * (2*n+5)) / (9*n*(n-1)));
t.dist = "stdnormal";
cdf = stdnormal_cdf (t.stat);
elseif (m == "s")
rho = spearman (x, y);
t.method = "Spearman's rank correlation rho";
t.params = [];
t.stat = sqrt (n-1) * (rho - 6/(n^3-n));
t.dist = "stdnormal";
cdf = stdnormal_cdf (t.stat);
else
error ("cor_test: METHOD '%s' not recognized", method);
endif
if (strcmp (alt, "!=") || strcmp (alt, "<>"))
t.pval = 2 * min (cdf, 1 - cdf);
elseif (strcmp (alt, ">"))
t.pval = 1 - cdf;
elseif (strcmp (alt, "<"))
t.pval = cdf;
else
error ("cor_test: alternative '%s' not recognized", alt);
endif
t.alternative = alt;
if (nargout == 0)
printf ("pval: %g\n", t.pval);
endif
endfunction
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