/usr/share/octave/packages/statistics-1.3.0/ztest.m is in octave-statistics 1.3.0-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 | ## Copyright (C) 2014 Tony Richardson
##
## 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 3 of the License, 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 program; if not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{h}, @var{pval}, @var{ci}, @var{z}, @var{zcrit}] =} ztest (@var{x}, @var{m}, @var{s})
## @deftypefnx {Function File} {[@var{h}, @var{pval}, @var{ci}, @var{z}, @var{zcrit}] =} ztest (@var{x}, @var{m}, @var{s}, @var{Name}, @var{Value})
## Test for mean of a normal sample with known variance.
##
## Perform a Z-test of the null hypothesis @code{mean (@var{x}) == @var{m}}
## for a sample @var{x} from a normal distribution with unknown
## mean and known std deviation @var{s}. Under the null, the test statistic
## @var{z} follows a standard normal distribution.
##
## Name-Value pair arguments can be used to set various options.
## @qcode{"alpha"} can be used to specify the significance level
## of the test (the default value is 0.05). @qcode{"tail"}, can be used
## to select the desired alternative hypotheses. If the value is
## @qcode{"both"} (default) the null is tested against the two-sided
## alternative @code{mean (@var{x}) != @var{m}}.
## If it is @qcode{"right"} the one-sided alternative @code{mean (@var{x})
## > @var{m}} is considered. Similarly for @qcode{"left"}, the one-sided
## alternative @code{mean (@var{x}) < @var{m}} is considered.
## When argument @var{x} is a matrix, @qcode{"dim"} can be used to selection
## the dimension over which to perform the test. (The default is the
## first non-singleton dimension.)
##
## If @var{h} is 0 the null hypothesis is accepted, if it is 1 the null
## hypothesis is rejected. The p-value of the test is returned in @var{pval}.
## A 100(1-alpha)% confidence interval is returned in @var{ci}. The test statistic
## value is returned in @var{z} and the z critical value in @var{zcrit}.
##
## @end deftypefn
## Author: Tony Richardson <richardson.tony@gmail.com>
function [h, p, ci, zval, zcrit] = ztest(x, m, sigma, varargin)
alpha = 0.05;
tail = 'both';
% Find the first non-singleton dimension of x
dim = min(find(size(x)~=1));
if isempty(dim), dim = 1; end
i = 1;
while ( i <= length(varargin) )
switch lower(varargin{i})
case 'alpha'
i = i + 1;
alpha = varargin{i};
case 'tail'
i = i + 1;
tail = varargin{i};
case 'dim'
i = i + 1;
dim = varargin{i};
otherwise
error('Invalid Name argument.',[]);
end
i = i + 1;
end
if ~isa(tail, 'char')
error('tail argument to ztest must be a string\n',[]);
end
% Calculate the test statistic value (zval)
n = size(x, dim);
x_bar = mean(x, dim);
x_bar_std = sigma/sqrt(n);
zval = (x_bar - m)./x_bar_std;
% Based on the "tail" argument determine the P-value, the critical values,
% and the confidence interval.
switch lower(tail)
case 'both'
p = 2*(1 - normcdf(abs(zval)));
zcrit = -norminv(alpha/2);
ci = [x_bar-zcrit*x_bar_std; x_bar+zcrit*x_bar_std];
case 'left'
p = normcdf(zval);
zcrit = -norminv(alpha);
ci = [-inf*ones(size(x_bar)); x_bar+zcrit*x_bar_std];
case 'right'
p = 1 - normcdf(zval);
zcrit = -norminv(alpha);
ci = [x_bar-zcrit*x_bar_std; inf*ones(size(x_bar))];
otherwise
error('Invalid fifth (tail) argument to ztest\n',[]);
end
% Reshape the ci array to match MATLAB shaping
if and(isscalar(x_bar), dim==2)
ci = ci(:)';
elseif size(x_bar,2)<size(x_bar,1)
ci = reshape(ci(:),length(x_bar),2);
end
% Determine the test outcome
% MATLAB returns this a double instead of a logical array
h = double(p < alpha);
end
|