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## Copyright (C) 1995, 1996, 1997 Kurt Hornik
##
## 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; either version 2, 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.
##
## You should have received a copy of the GNU General Public License
## along with this file. If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
## usage: [pval, t, df] = t_test (x, m [, alt])
##
## For a sample x from a normal distribution with unknown mean and
## variance, perform a t-test of the null hypothesis mean(x) == m.
## Under the null, the test statistic t follows a Student distribution
## with df = length (x) - 1 degrees of freedom.
##
## With the optional argument string alt, the alternative of interest
## can be selected.
## If alt is "!=" or "<>", the null is tested against the two-sided
## alternative mean(x) != m.
## If alt is ">", the one-sided alternative mean(x) > m is considered,
## similarly for "<".
## The default is the two-sided case.
##
## pval is the p-value of the test.
##
## If no output argument is given, the p-value of the test is displayed.
## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description: Student's one-sample t test
function [pval, t, df] = t_test (x, m, alt)
if ((nargin < 2) || (nargin > 3))
usage ("[pval, t, df] = t_test (x, m [, alt])");
endif
if (! is_vector (x))
error ("t_test: x must be a vector.");
endif
if (! is_scalar (m))
error ("t_test: m must be a scalar.");
endif
n = length (x);
df = n - 1;
t = sqrt (n) * (sum (x) / n - m) / std (x);
cdf = t_cdf (t, df);
if (nargin == 2)
alt = "!=";
endif
if (! isstr (alt))
error ("t_test: alt must be a string");
endif
if (strcmp (alt, "!=") || strcmp (alt, "<>"))
pval = 2 * min (cdf, 1 - cdf);
elseif strcmp (alt, ">")
pval = 1 - cdf;
elseif strcmp (alt, "<")
pval = cdf;
else
error (sprintf ("t_test: option %s not recognized", alt));
endif
if (nargout == 0)
printf (" pval: %g\n", pval);
endif
endfunction
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