Mercurial > octave-nkf
annotate scripts/statistics/tests/t_test.m @ 20209:d9341b422488 stable
doc: Update more docstrings to have one sentence summary as first line.
Reviewed statistics/ and @ftp/ in scripts directory.
* scripts/@ftp/ascii.m, scripts/@ftp/binary.m, scripts/@ftp/cd.m,
scripts/@ftp/dir.m, scripts/@ftp/ftp.m, scripts/@ftp/mget.m,
scripts/@ftp/mput.m, scripts/statistics/base/center.m,
scripts/statistics/base/cloglog.m, scripts/statistics/base/cov.m,
scripts/statistics/base/gls.m, scripts/statistics/base/histc.m,
scripts/statistics/base/iqr.m, scripts/statistics/base/kendall.m,
scripts/statistics/base/kurtosis.m, scripts/statistics/base/logit.m,
scripts/statistics/base/lscov.m, scripts/statistics/base/mahalanobis.m,
scripts/statistics/base/mean.m, scripts/statistics/base/meansq.m,
scripts/statistics/base/median.m, scripts/statistics/base/mode.m,
scripts/statistics/base/moment.m, scripts/statistics/base/ols.m,
scripts/statistics/base/ppplot.m, scripts/statistics/base/prctile.m,
scripts/statistics/base/probit.m, scripts/statistics/base/range.m,
scripts/statistics/base/ranks.m, scripts/statistics/base/run_count.m,
scripts/statistics/base/runlength.m, scripts/statistics/base/skewness.m,
scripts/statistics/base/spearman.m, scripts/statistics/base/statistics.m,
scripts/statistics/base/std.m, scripts/statistics/base/table.m,
scripts/statistics/base/var.m, scripts/statistics/base/zscore.m,
scripts/statistics/distributions/betainv.m,
scripts/statistics/distributions/binoinv.m,
scripts/statistics/distributions/binopdf.m,
scripts/statistics/distributions/cauchy_cdf.m,
scripts/statistics/distributions/cauchy_inv.m,
scripts/statistics/distributions/cauchy_pdf.m,
scripts/statistics/distributions/chi2cdf.m,
scripts/statistics/distributions/chi2inv.m,
scripts/statistics/distributions/chi2pdf.m,
scripts/statistics/distributions/discrete_cdf.m,
scripts/statistics/distributions/discrete_inv.m,
scripts/statistics/distributions/discrete_pdf.m,
scripts/statistics/distributions/empirical_cdf.m,
scripts/statistics/distributions/empirical_inv.m,
scripts/statistics/distributions/empirical_pdf.m,
scripts/statistics/distributions/expcdf.m,
scripts/statistics/distributions/expinv.m,
scripts/statistics/distributions/exppdf.m,
scripts/statistics/distributions/finv.m,
scripts/statistics/distributions/fpdf.m,
scripts/statistics/distributions/gamcdf.m,
scripts/statistics/distributions/gaminv.m,
scripts/statistics/distributions/gampdf.m,
scripts/statistics/distributions/geoinv.m,
scripts/statistics/distributions/geopdf.m,
scripts/statistics/distributions/hygecdf.m,
scripts/statistics/distributions/hygeinv.m,
scripts/statistics/distributions/hygepdf.m,
scripts/statistics/distributions/kolmogorov_smirnov_cdf.m,
scripts/statistics/distributions/laplace_cdf.m,
scripts/statistics/distributions/laplace_inv.m,
scripts/statistics/distributions/laplace_pdf.m,
scripts/statistics/distributions/logistic_inv.m,
scripts/statistics/distributions/logncdf.m,
scripts/statistics/distributions/logninv.m,
scripts/statistics/distributions/lognpdf.m,
scripts/statistics/distributions/nbincdf.m,
scripts/statistics/distributions/nbininv.m,
scripts/statistics/distributions/nbinpdf.m,
scripts/statistics/distributions/nbinrnd.m,
scripts/statistics/distributions/normcdf.m,
scripts/statistics/distributions/norminv.m,
scripts/statistics/distributions/normpdf.m,
scripts/statistics/distributions/poisscdf.m,
scripts/statistics/distributions/poissinv.m,
scripts/statistics/distributions/poisspdf.m,
scripts/statistics/distributions/stdnormal_cdf.m,
scripts/statistics/distributions/stdnormal_pdf.m,
scripts/statistics/distributions/tcdf.m,
scripts/statistics/distributions/tinv.m,
scripts/statistics/distributions/tpdf.m,
scripts/statistics/distributions/unidcdf.m,
scripts/statistics/distributions/unidinv.m,
scripts/statistics/distributions/unidpdf.m,
scripts/statistics/distributions/unidrnd.m,
scripts/statistics/distributions/unifcdf.m,
scripts/statistics/distributions/unifinv.m,
scripts/statistics/distributions/wblcdf.m,
scripts/statistics/distributions/wblinv.m,
scripts/statistics/distributions/wblpdf.m,
scripts/statistics/distributions/wienrnd.m,
scripts/statistics/models/private/logistic_regression_derivatives.m,
scripts/statistics/models/private/logistic_regression_likelihood.m,
scripts/statistics/tests/anova.m,
scripts/statistics/tests/chisquare_test_homogeneity.m,
scripts/statistics/tests/chisquare_test_independence.m,
scripts/statistics/tests/cor_test.m,
scripts/statistics/tests/f_test_regression.m,
scripts/statistics/tests/hotelling_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test_2.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/manova.m, scripts/statistics/tests/mcnemar_test.m,
scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/run_test.m,
scripts/statistics/tests/sign_test.m, scripts/statistics/tests/t_test.m,
scripts/statistics/tests/t_test_2.m,
scripts/statistics/tests/t_test_regression.m,
scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m,
scripts/statistics/tests/welch_test.m,
scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m,
scripts/statistics/tests/z_test_2.m:
Update more docstrings to have one sentence summary as first line.
author | Rik <rik@octave.org> |
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date | Sun, 10 May 2015 16:07:41 -0700 |
parents | 9fc020886ae9 |
children | aa36fb998a4d |
rev | line source |
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1 ## Copyright (C) 1995-2015 Kurt Hornik |
3426 | 2 ## |
3922 | 3 ## This file is part of Octave. |
4 ## | |
5 ## Octave is free software; you can redistribute it and/or modify it | |
6 ## under the terms of the GNU General Public License as published by | |
7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
8 ## your option) any later version. | |
3426 | 9 ## |
3922 | 10 ## Octave is distributed in the hope that it will be useful, but |
3200 | 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
3426 | 13 ## General Public License for more details. |
14 ## | |
3200 | 15 ## You should have received a copy of the GNU General Public License |
7016 | 16 ## along with Octave; see the file COPYING. If not, see |
17 ## <http://www.gnu.org/licenses/>. | |
3200 | 18 |
3454 | 19 ## -*- texinfo -*- |
20 ## @deftypefn {Function File} {[@var{pval}, @var{t}, @var{df}] =} t_test (@var{x}, @var{m}, @var{alt}) | |
21 ## For a sample @var{x} from a normal distribution with unknown mean and | |
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22 ## variance, perform a t-test of the null hypothesis |
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23 ## @code{mean (@var{x}) == @var{m}}. |
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24 ## |
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25 ## Under the null, the test statistic @var{t} follows a Student distribution |
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26 ## with @code{@var{df} = length (@var{x}) - 1} degrees of freedom. |
3200 | 27 ## |
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28 ## With the optional argument string @var{alt}, the alternative of interest |
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29 ## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null |
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30 ## is tested against the two-sided alternative @code{mean (@var{x}) != |
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31 ## @var{m}}. If @var{alt} is @qcode{">"}, the one-sided alternative |
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32 ## @code{mean (@var{x}) > @var{m}} is considered. Similarly for @var{"<"}, |
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33 ## the one-sided alternative @code{mean (@var{x}) < @var{m}} is considered. |
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34 ## The default is the two-sided case. |
3200 | 35 ## |
3454 | 36 ## The p-value of the test is returned in @var{pval}. |
3426 | 37 ## |
3200 | 38 ## If no output argument is given, the p-value of the test is displayed. |
3454 | 39 ## @end deftypefn |
3426 | 40 |
5428 | 41 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
3456 | 42 ## Description: Student's one-sample t test |
3200 | 43 |
44 function [pval, t, df] = t_test (x, m, alt) | |
3426 | 45 |
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46 if (nargin < 2 || nargin > 3) |
6046 | 47 print_usage (); |
3200 | 48 endif |
3426 | 49 |
4030 | 50 if (! isvector (x)) |
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51 error ("t_test: X must be a vector"); |
3200 | 52 endif |
4030 | 53 if (! isscalar (m)) |
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54 error ("t_test: M must be a scalar"); |
3200 | 55 endif |
3426 | 56 |
3200 | 57 n = length (x); |
58 df = n - 1; | |
59 t = sqrt (n) * (sum (x) / n - m) / std (x); | |
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60 cdf = tcdf (t, df); |
3426 | 61 |
3200 | 62 if (nargin == 2) |
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63 alt = "!="; |
3200 | 64 endif |
65 | |
5443 | 66 if (! ischar (alt)) |
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67 error ("t_test: ALT must be a string"); |
3200 | 68 endif |
69 if (strcmp (alt, "!=") || strcmp (alt, "<>")) | |
70 pval = 2 * min (cdf, 1 - cdf); | |
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71 elseif (strcmp (alt, ">")) |
3200 | 72 pval = 1 - cdf; |
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73 elseif (strcmp (alt, "<")) |
3200 | 74 pval = cdf; |
75 else | |
3456 | 76 error ("t_test: option %s not recognized", alt); |
3200 | 77 endif |
78 | |
79 if (nargout == 0) | |
3456 | 80 printf (" pval: %g\n", pval); |
3200 | 81 endif |
3426 | 82 |
3200 | 83 endfunction |
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84 |
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85 |
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86 %!test |
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87 %! ## Two-sided (also the default option) |
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88 %! x = rand (10,1); n = length (x); |
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89 %! u0 = 0.5; # true mean |
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90 %! xbar = mean (x); |
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91 %! pval = t_test (x, u0, "!="); |
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92 %! if (xbar >= u0) |
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93 %! tval = abs (tinv (0.5*pval, n-1)); |
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94 %! else |
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95 %! tval = -abs (tinv (0.5*pval, n-1)); |
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96 %! endif |
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97 %! unew = tval * std(x)/sqrt(n) + u0; |
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98 %! assert (xbar, unew, 100*eps); |
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99 |
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100 %!test |
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101 %! x = rand (10,1); n = length (x); |
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102 %! u0 = 0.5; |
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103 %! pval = t_test (x, u0, ">"); |
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104 %! tval = tinv (1-pval, n-1); |
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105 %! unew = tval * std(x)/sqrt(n) + u0; |
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106 %! assert (mean (x), unew, 100*eps); |
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107 |
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108 %!test |
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109 %! x = rand (10,1); n = length (x); |
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110 %! u0 = 0.5; |
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111 %! pval = t_test (x, u0, "<"); |
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112 %! tval = tinv (pval, n-1); |
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113 %! unew = tval * std(x)/sqrt(n) + u0; |
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114 %! assert (mean (x), unew, 100*eps); |
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115 |