/usr/share/octave/packages/statistics-1.3.0/binotest.m is in octave-statistics 1.3.0-1.
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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 | ## Copyright (C) 2016 Andreas Stahel
##
## 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}] =} binotest (@var{pos},@var{N},@var{p0})
## @deftypefnx {Function File} {[@var{h}, @var{pval}, @var{ci}] =} binotest (@var{pos},@var{N},@var{p0},@var{Name},@var{Value})
## Test for probability @var{p} of a binomial sample
##
## Perform a test of the null hypothesis @var{p} == @var{p0} for a sample
## of size @var{N} with @var{pos} positive results
##
##
## 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). The option @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{@var{p} != @var{p0}}. The value of @var{pval} is
## determined by adding the probabilities of all event less or equally
## likely than the observed number @var{pos} of positive events.
## If the value of @qcode{"tail"} is @qcode{"right"}
## the one-sided alternative @code{@var{p} > @var{p0}} is considered.
## Similarly for @qcode{"left"}, the one-sided alternative
## @code{@var{p} < @var{p0}} is considered.
##
## 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}.
##
## @end deftypefn
## Author: Andreas Stahel <Andreas.Stahel@bfh.ch.
## based on the code ttest.m by Tony Richardson <richardson.tony@gmail.com>
function [h, p, ci] = binotest(pos,n,p0,varargin)
% Set default arguments
alpha = 0.05;
tail = 'both';
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};
otherwise
error('Invalid Name argument.',[]);
end
i = i + 1;
end
if ~isa(tail,'char')
error('tail argument to vartest must be a string\n',[]);
end
if (n<=0)
error('binotest: required n>0\n',[]);
end
if (p0<0)|(p0>1)
error('binotest: required 0<= p0 <= 1\n',[]);
end
if (pos<0)|(pos>n)
error('binotest: required 0<= pos <= n\n',[]);
end
% Based on the "tail" argument determine the P-value, the critical values,
% and the confidence interval.
switch lower(tail)
case 'both'
A_low = binoinv(alpha/2,n,p0)/n;
A_high = binoinv(1-alpha/2,n,p0)/n;
p_pos = binopdf(pos,n,p0);
p_all = binopdf([0:n],n,p0);
ind = find(p_all <=p_pos);
% p = min(1,sum(p_all(ind)));
p = sum(p_all(ind));
if pos==0 p_low = 0;
else p_low = fzero(@(pl)1-binocdf(pos-1,n,pl)-alpha/2,[0 1]);
endif
if pos==n p_high = 1;
else p_high = fzero(@(ph) binocdf(pos,n,ph) -alpha/2,[0,1]);
endif
ci = [p_low,p_high];
case 'left'
p = 1-binocdf(pos-1,n,p0);
if pos==n p_high = 1;
else p_high = fzero(@(ph) binocdf(pos,n,ph) -alpha,[0,1]);
endif
ci = [0, p_high];
case 'right'
p = binocdf(pos,n,p0);
if pos==0 p_low = 0;
else p_low = fzero(@(pl)1-binocdf(pos-1,n,pl)-alpha,[0 1]);
endif
ci = [p_low 1];
otherwise
error('Invalid fifth (tail) argument to binotest\n',[]);
end
% Determine the test outcome
% MATLAB returns this a double instead of a logical array
h = double(p < alpha);
end
%!demo
%! % flip a coin 1000 times, showing 475 heads
%! % Hypothesis: coin is fair, i.e. p=1/2
%! [h,p_val,ci] = binotest(475,1000,0.5)
%! % Result: h = 0 : null hypothesis not rejected, coin could be fair
%! % P value 0.12, i.e. hypothesis not rejected for alpha up to 12%
%! % 0.444 <= p <= 0.506 with 95% confidence
%!demo
%! % flip a coin 100 times, showing 65 heads
%! % Hypothesis: coin shows less than 50% heads, i.e. p<=1/2
%! [h,p_val,ci] = binotest(65,100,0.5,'tail','left','alpha',0.01)
%! % Result: h = 1 : null hypothesis is rejected, i.e. coin shows more heads than tails
%! % P value 0.0018, i.e. hypothesis not rejected for alpha up to 0.18%
%! % 0 <= p <= 0.76 with 99% confidence
%!test #example from https://en.wikipedia.org/wiki/Binomial_test
%! [h,p_val,ci] = binotest (51,235,1/6);
%! assert (p_val, 0.0437, 0.00005)
%! [h,p_val,ci] = binotest (51,235,1/6,'tail','left');
%! assert (p_val, 0.027, 0.0005)
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