octave: scripts/statistics/tests/t

annotate scripts/statistics/tests/t_test.m @ 21634:96518f623c91

Backed out changeset dcf8922b724b

author	Mike Miller <mtmiller@octave.org>
date	Wed, 20 Apr 2016 11:06:03 -0700
parents	dcf8922b724b
children	bac0d6f07a3e

rev	line source
19697 4197fc428c7d maint: Update copyright notices for 2015. John W. Eaton <jwe@octave.org> parents: 19306 diff changeset	1 ## Copyright (C) 1995-2015 Kurt Hornik
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	2 ##
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3458 diff changeset	3 ## This file is part of Octave.
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3458 diff changeset	4 ##
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3458 diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3458 diff changeset	6 ## under the terms of the GNU General Public License as published by
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7001 diff changeset	7 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7001 diff changeset	8 ## your option) any later version.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	9 ##
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3458 diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	13 ## General Public License for more details.
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	14 ##
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	15 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7001 diff changeset	16 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 7001 diff changeset	17 ## <http://www.gnu.org/licenses/>.
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	18
3454 d8b731d3f7a3 [project @ 2000-01-18 10:13:31 by jwe] jwe parents: 3426 diff changeset	19 ## -- texinfo --
20852 516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20181 diff changeset	20 ## @deftypefn {} {[@var{pval}, @var{t}, @var{df}] =} t_test (@var{x}, @var{m}, @var{alt})
3454 d8b731d3f7a3 [project @ 2000-01-18 10:13:31 by jwe] jwe parents: 3426 diff changeset	21 ## For a sample @var{x} from a normal distribution with unknown mean and
20174 d9341b422488 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	22 ## variance, perform a t-test of the null hypothesis
d9341b422488 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	23 ## @code{mean (@var{x}) == @var{m}}.
d9341b422488 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	24 ##
d9341b422488 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	25 ## Under the null, the test statistic @var{t} follows a Student distribution
d9341b422488 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	26 ## with @code{@var{df} = length (@var{x}) - 1} degrees of freedom.
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	27 ##
20174 d9341b422488 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	28 ## With the optional argument string @var{alt}, the alternative of interest
d9341b422488 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	29 ## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null
d9341b422488 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	30 ## is tested against the two-sided alternative @code{mean (@var{x}) !=
d9341b422488 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	31 ## @var{m}}. If @var{alt} is @qcode{">"}, the one-sided alternative
d9341b422488 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	32 ## @code{mean (@var{x}) > @var{m}} is considered. Similarly for @var{"<"},
20181 aa36fb998a4d maint: Remove unnecessary whitespace at end of lines. Rik <rik@octave.org> parents: 20174 diff changeset	33 ## the one-sided alternative @code{mean (@var{x}) < @var{m}} is considered.
20174 d9341b422488 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	34 ## The default is the two-sided case.
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	35 ##
3454 d8b731d3f7a3 [project @ 2000-01-18 10:13:31 by jwe] jwe parents: 3426 diff changeset	36 ## The p-value of the test is returned in @var{pval}.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	37 ##
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	38 ## If no output argument is given, the p-value of the test is displayed.
3454 d8b731d3f7a3 [project @ 2000-01-18 10:13:31 by jwe] jwe parents: 3426 diff changeset	39 ## @end deftypefn
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	40
5428 2a16423e4aa0 [project @ 2005-08-23 18:38:27 by jwe] jwe parents: 5307 diff changeset	41 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
3456 434790acb067 [project @ 2000-01-19 06:58:51 by jwe] jwe parents: 3454 diff changeset	42 ## Description: Student's one-sample t test
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	43
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	44 function [pval, t, df] = t_test (x, m, alt)
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	45
19833 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19697 diff changeset	46 if (nargin < 2 \|\| nargin > 3)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5443 diff changeset	47 print_usage ();
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	48 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	49
4030 22bd65326ec1 [project @ 2002-08-09 18:58:13 by jwe] jwe parents: 3922 diff changeset	50 if (! isvector (x))
11472 1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done. Rik <octave@nomad.inbox5.com> parents: 10606 diff changeset	51 error ("t_test: X must be a vector");
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	52 endif
4030 22bd65326ec1 [project @ 2002-08-09 18:58:13 by jwe] jwe parents: 3922 diff changeset	53 if (! isscalar (m))
11472 1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done. Rik <octave@nomad.inbox5.com> parents: 10606 diff changeset	54 error ("t_test: M must be a scalar");
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	55 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	56
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	57 n = length (x);
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	58 df = n - 1;
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	59 t = sqrt (n) * (sum (x) / n - m) / std (x);
10606 ec34c7acd057 Replace deprecated function calls in statistics tests Rik <octave@nomad.inbox5.com> parents: 7017 diff changeset	60 cdf = tcdf (t, df);
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	61
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	62 if (nargin == 2)
19833 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19697 diff changeset	63 alt = "!=";
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	64 endif
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	65
5443 ec8c33dcd1bf [project @ 2005-09-08 01:40:57 by jwe] jwe parents: 5428 diff changeset	66 if (! ischar (alt))
11472 1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done. Rik <octave@nomad.inbox5.com> parents: 10606 diff changeset	67 error ("t_test: ALT must be a string");
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	68 endif
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	69 if (strcmp (alt, "!=") \|\| strcmp (alt, "<>"))
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	70 pval = 2 * min (cdf, 1 - cdf);
14552 86854d032a37 maint: miscellaneous style fixes for .m files John W. Eaton <jwe@octave.org> parents: 14138 diff changeset	71 elseif (strcmp (alt, ">"))
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	72 pval = 1 - cdf;
14552 86854d032a37 maint: miscellaneous style fixes for .m files John W. Eaton <jwe@octave.org> parents: 14138 diff changeset	73 elseif (strcmp (alt, "<"))
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	74 pval = cdf;
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	75 else
3456 434790acb067 [project @ 2000-01-19 06:58:51 by jwe] jwe parents: 3454 diff changeset	76 error ("t_test: option %s not recognized", alt);
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	77 endif
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	78
781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	79 if (nargout == 0)
21634 96518f623c91 Backed out changeset dcf8922b724b Mike Miller <mtmiller@octave.org> parents: 21633 diff changeset	80 printf (" pval: %g\n", pval);
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	81 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3200 diff changeset	82
3200 781c930425fd [project @ 1998-10-29 05:23:08 by jwe] jwe parents: diff changeset	83 endfunction
17338 1c89599167a6 maint: End m-files with 1 blank line. Rik <rik@octave.org> parents: 17281 diff changeset	84
19306 314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	85
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	86 %!test
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	87 %! ## Two-sided (also the default option)
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	88 %! x = rand (10,1); n = length (x);
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	89 %! u0 = 0.5; # true mean
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	90 %! xbar = mean (x);
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	91 %! pval = t_test (x, u0, "!=");
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	92 %! if (xbar >= u0)
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	93 %! tval = abs (tinv (0.5*pval, n-1));
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	94 %! else
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	95 %! tval = -abs (tinv (0.5*pval, n-1));
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	96 %! endif
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	97 %! unew = tval * std(x)/sqrt(n) + u0;
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	98 %! assert (xbar, unew, 100*eps);
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	99
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	100 %!test
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	101 %! x = rand (10,1); n = length (x);
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	102 %! u0 = 0.5;
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	103 %! pval = t_test (x, u0, ">");
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	104 %! tval = tinv (1-pval, n-1);
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	105 %! unew = tval * std(x)/sqrt(n) + u0;
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	106 %! assert (mean (x), unew, 100*eps);
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	107
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	108 %!test
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	109 %! x = rand (10,1); n = length (x);
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	110 %! u0 = 0.5;
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	111 %! pval = t_test (x, u0, "<");
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	112 %! tval = tinv (pval, n-1);
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	113 %! unew = tval * std(x)/sqrt(n) + u0;
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	114 %! assert (mean (x), unew, 100*eps);
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	115

Mercurial > octave

annotate scripts/statistics/tests/t_test.m @ 21634:96518f623c91