/usr/share/octave/packages/statistics-1.3.0/signtest.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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 | ## 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{pval}, @var{h}, @var{stats}] =} signtest (@var{x})
## @deftypefnx {Function File} {[@var{pval}, @var{h}, @var{stats}] =} signtest (@var{x}, @var{m})
## @deftypefnx {Function File} {[@var{pval}, @var{h}, @var{stats}] =} signtest (@var{x}, @var{y})
## @deftypefnx {Function File} {[@var{pval}, @var{h}, @var{stats}] =} signtest (@var{x}, @var{y}, @var{Name}, @var{Value})
## Test for median.
##
## Perform a signtest of the null hypothesis that @var{x} is from a distribution
## that has a zero median.
##
## If the second argument @var{m} is a scalar, the null hypothesis is that
## X has median m.
##
## If the second argument @var{y} is a vector, the null hypothesis is that
## the distribution of @code{@var{x} - @var{y}} has zero median.
##
## The argument @qcode{"alpha"} can be used to specify the significance level
## of the test (the default value is 0.05). The string
## argument @qcode{"tail"}, can be used to select the desired alternative
## hypotheses. If @qcode{"alt"} is @qcode{"both"} (default) the null is
## tested against the two-sided alternative @code{median (@var{x}) != @var{m}}.
## If @qcode{"alt"} is @qcode{"right"} the one-sided
## alternative @code{median (@var{x}) > @var{m}} is considered.
## Similarly for @qcode{"left"}, the one-sided alternative @code{median
## (@var{x}) < @var{m}} is considered. When @qcode{"method"} is @qcode{"exact"}
## the p-value is computed using an exact method (this is the default). When
## @qcode{"method"} is @qcode{"approximate"} a normal approximation is used for the
## test statistic.
##
## The p-value of the test is returned in @var{pval}. If @var{h} is 0 the
## null hypothesis is accepted, if it is 1 the null hypothesis is rejected.
## @var{stats} is a structure containing the value of the test statistic
## (@var{sign}) and the value of the z statistic (@var{zval}) (only computed
## when the 'method' is 'approximate'.
##
## @end deftypefn
## Author: Tony Richardson <richardson.tony@gmail.com>
function [p, h, stats] = signtest(x, my, varargin)
my_default = 0;
alpha = 0.05;
tail = 'both';
method = 'exact';
% Find the first non-singleton dimension of x
dim = min(find(size(x)~=1));
if isempty(dim), dim = 1; end
if (nargin == 1)
my = my_default;
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 'method'
i = i + 1;
method = 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 signtest must be a string\n',[]);
end
if ~isa(method, 'char')
error('method argument to signtest must be a string\n',[]);
end
% Set default values if arguments are present but empty
if isempty(my)
my = my_default;
end
% This adjustment allows everything else to remain the
% same for both the one-sample t test and paired tests.
% If second argument is a vector
if ~isscalar(my)
x = x - my;
my = my_default;
end
n = size(x, dim);
switch lower(method)
case 'exact'
stats.zval = nan;
switch lower(tail)
case 'both'
w = min(sum(x<my),sum(x>my));
pl = binocdf(w, n, 0.5);
p = 2*min(pl,1-pl);
case 'left'
w = sum(x<my);
p = binocdf(w, n, 0.5);
case 'right'
w = sum(x>my);
p = 1 - binocdf(w, n, 0.5);
otherwise
error('Invalid tail argument to signtest\n',[]);
end
case 'approximate'
switch lower(tail)
case 'both'
npos = sum(x>my);
nneg = sum(x<my);
w = min(npos,nneg);
stats.zval = (w - 0.5*n - 0.5*sign(npos-nneg))/sqrt(0.25*n);
pl = normcdf(stats.zval);
p = 2*min(pl,1-pl);
case 'left'
npos = sum(x>my);
nneg = sum(x<my);
w = sum(x<my);
stats.zval = (w - 0.5*n - 0.5*sign(npos-nneg))/sqrt(0.25*n);
p = normcdf(stats.zval);
case 'right'
npos = sum(x>my);
nneg = sum(x<my);
w = sum(x>my);
stats.zval = (w - 0.5*n - 0.5*sign(npos-nneg))/sqrt(0.25*n);
p = 1-normcdf(stats.zval);
otherwise
error('Invalid tail argument to signtest\n',[]);
end
otherwise
error('Invalid method argument to signtest\n',[]);
end
stats.sign = w;
h = double(p < alpha);
end
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