## Copyright (C) 1996-2012 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}] =} prop_test_2 (@var{x1}, @var{n1}, @var{x2}, @var{n2}, @var{alt})
## If @var{x1} and @var{n1} are the counts of successes and trials in
## one sample, and @var{x2} and @var{n2} those in a second one, test the
## null hypothesis that the success probabilities @var{p1} and @var{p2}
## are the same.  Under the null, the test statistic @var{z}
## approximately 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
## @var{p1} != @var{p2}.  If @var{alt} is @qcode{">"}, the one-sided
## alternative @var{p1} > @var{p2} is used.  Similarly for @qcode{"<"},
## the one-sided alternative @var{p1} < @var{p2} 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.
## @end deftypefn

## Author: KH <Kurt.Hornik@wu-wien.ac.at>
## Description: Compare two proportions

function [pval, z] = prop_test_2 (x1, n1, x2, n2, alt)

  if ((nargin < 4) || (nargin > 5))
        print_usage ();
  endif

  ## Could do sanity checking on x1, n1, x2, n2 here

  p1  = x1 / n1;
  p2  = x2 / n2;
  pc  = (x1 + x2) / (n1 + n2);

  z   = (p1 - p2) / sqrt (pc * (1 - pc) * (1/n1 + 1/n2));

  cdf = stdnormal_cdf (z);

  if (nargin == 4)
    alt  = "!=";
  endif

  if (! ischar (alt))
    error ("prop_test_2: 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 ("prop_test_2: option %s not recognized", alt);
  endif

  if (nargout == 0)
    printf ("  pval: %g\n", pval);
  endif

endfunction