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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} {[@var{pval}, @var{z}] =} z_test_2 (@var{x}, @var{y}, @var{v_x}, @var{v_y}, @var{alt})
## For two samples @var{x} and @var{y} from normal distributions with unknown
## means and known variances @var{v_x} and @var{v_y}, perform a Z-test of the
## hypothesis of equal means.
##
## Under the null, the test statistic @var{z} follows a standard normal
## distribution.
##
## With the optional argument string @var{alt}, the alternative of interest
## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null
## is tested against the two-sided alternative
## @code{mean (@var{x}) != mean (@var{y})}. If alt is @qcode{">"}, the
## one-sided alternative @code{mean (@var{x}) > mean (@var{y})} is used.
## Similarly for @qcode{"<"}, the one-sided alternative
## @code{mean (@var{x}) < mean (@var{y})} is used. The default is the
## two-sided case.
##
## The p-value of the test is returned in @var{pval}.
##
## If no output argument is given, the p-value of the test is displayed along
## with some information.
## @end deftypefn
## Author: KH <Kurt.Hornik@wu-wien.ac.at>
## Description: Compare means of two normal samples with known variances
function [pval, z] = z_test_2 (x, y, v_x, v_y, alt)
if (nargin < 4 || nargin > 5)
print_usage ();
endif
if (! (isvector (x) && isvector (y)))
error ("z_test_2: both X and Y must be vectors");
elseif (! (isscalar (v_x) && (v_x > 0)
&& isscalar (v_y) && (v_y > 0)))
error ("z_test_2: both V_X and V_Y must be positive scalars");
endif
n_x = length (x);
n_y = length (y);
mu_x = sum (x) / n_x;
mu_y = sum (y) / n_y;
z = (mu_x - mu_y) / sqrt (v_x / n_x + v_y / n_y);
cdf = stdnormal_cdf (z);
if (nargin == 4)
alt = "!=";
endif
if (! ischar (alt))
error ("z_test_2: ALT must be a string");
elseif (strcmp (alt, "!=") || strcmp (alt, "<>"))
pval = 2 * min (cdf, 1 - cdf);
elseif (strcmp (alt, ">"))
pval = 1 - cdf;
elseif (strcmp (alt, "<"))
pval = cdf;
else
error ("z_test_2: option %s not recognized", alt);
endif
if (nargout == 0)
s = ["Two-sample Z-test of mean(x) == mean(y) against ", ...
"mean(x) %s mean(y),\n", ...
"with known var(x) == %g and var(y) == %g:\n", ...
" pval = %g\n"];
printf (s, alt, v_x, v_y, pval);
endif
endfunction
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