update packages

[CreaPhase.git] / octave_packages / m / statistics / tests / z_test_2.m

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+## Copyright (C) 1995-2012 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 @code{"!="} or
+## @code{"<>"}, the null is tested against the two-sided alternative
+## @code{mean (@var{x}) != mean (@var{y})}.  If alt is @code{">"}, the
+## one-sided alternative @code{mean (@var{x}) > mean (@var{y})} is used.
+## Similarly for @code{"<"}, 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 = cstrcat ("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