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scripts/statistics/tests/z_test.m

changeset 10289: 4b124317dc38
parent:3422f39573b1
author: John W. Eaton <jwe@octave.org>
date: Tue Feb 09 20:58:55 2010 -0500 (35 minutes ago)
permissions: -rw-r--r--
description: base_properties::set_children: account for hidden children 
     1## Copyright (C) 1995, 1996, 1997, 1998, 2000, 2002, 2005, 2006, 2007, 2008

     2##               Kurt Hornik

     3##

     4## This file is part of Octave.

     5##

     6## Octave is free software; you can redistribute it and/or modify it

     7## under the terms of the GNU General Public License as published by

     8## the Free Software Foundation; either version 3 of the License, or (at

     9## your option) any later version.

    10##

    11## Octave is distributed in the hope that it will be useful, but

    12## WITHOUT ANY WARRANTY; without even the implied warranty of

    13## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

    14## General Public License for more details.

    15##

    16## You should have received a copy of the GNU General Public License

    17## along with Octave; see the file COPYING.  If not, see

    18## <http://www.gnu.org/licenses/>.

    19

    20## -*- texinfo -*-

    21## @deftypefn {Function File} {[@var{pval}, @var{z}] =} z_test (@var{x}, @var{m}, @var{v}, @var{alt})

    22## Perform a Z-test of the null hypothesis @code{mean (@var{x}) ==

    23## @var{m}} for a sample @var{x} from a normal distribution with unknown

    24## mean and known variance @var{v}.  Under the null, the test statistic

    25## @var{z} follows a standard normal distribution.

    26##

    27## With the optional argument string @var{alt}, the alternative of

    28## interest can be selected.  If @var{alt} is @code{"!="} or

    29## @code{"<>"}, the null is tested against the two-sided alternative

    30## @code{mean (@var{x}) != @var{m}}.  If @var{alt} is @code{">"}, the

    31## one-sided alternative @code{mean (@var{x}) > @var{m}} is considered.

    32## Similarly for @code{"<"}, the one-sided alternative @code{mean

    33## (@var{x}) < @var{m}} is considered.  The default is the two-sided

    34## case.

    35##

    36## The p-value of the test is returned in @var{pval}.

    37##

    38## If no output argument is given, the p-value of the test is displayed

    39## along with some information.

    40## @end deftypefn

    41

    42## Author: KH <Kurt.Hornik@wu-wien.ac.at>

    43## Description: Test for mean of a normal sample with known variance

    44

    45function [pval, z] = z_test (x, m, v, alt)

    46

    47  if ((nargin < 3) || (nargin > 4))

    48    print_usage ();

    49  endif

    50

    51  if (! isvector (x))

    52    error ("z_test: x must be a vector");

    53  endif

    54  if (! isscalar (m))

    55    error ("z_test: m must be a scalar");

    56  endif

    57  if (! (isscalar (v) && (v > 0)))

    58    error ("z_test: v must be a positive scalar");

    59  endif

    60

    61  n = length (x);

    62  z = sqrt (n/v) * (sum (x) / n - m);

    63  cdf = stdnormal_cdf (z);

    64

    65  if (nargin == 3)

    66    alt = "!=";

    67  endif

    68

    69  if (! ischar (alt))

    70    error ("z_test: alt must be a string");

    71  elseif (strcmp (alt, "!=") || strcmp (alt, "<>"))

    72    pval = 2 * min (cdf, 1 - cdf);

    73  elseif (strcmp (alt, ">"))

    74    pval = 1 - cdf;

    75  elseif (strcmp (alt, "<"))

    76    pval = cdf;

    77  else

    78    error ("z_test: option %s not recognized", alt);

    79  endif

    80

    81  if (nargout == 0)

    82    s = cstrcat ("Z-test of mean(x) == %g against mean(x) %s %g,\n",

    83                "with known var(x) == %g:\n",

    84                "  pval = %g\n");

    85    printf (s, m, alt, m, v, pval);

    86  endif

    87

    88endfunction