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1 ## Copyright (C) 1995, 1996, 1997, 1998, 2000, 2002, 2005, 2006, 2007 |
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2 ## Kurt Hornik |
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3 ## |
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4 ## This file is part of Octave. |
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5 ## |
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6 ## Octave is free software; you can redistribute it and/or modify it |
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7 ## under the terms of the GNU General Public License as published by |
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8 ## the Free Software Foundation; either version 3 of the License, or (at |
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9 ## your option) any later version. |
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10 ## |
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11 ## Octave is distributed in the hope that it will be useful, but |
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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14 ## General Public License for more details. |
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15 ## |
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16 ## You should have received a copy of the GNU General Public License |
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17 ## along with Octave; see the file COPYING. If not, see |
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18 ## <http://www.gnu.org/licenses/>. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {[@var{pval}, @var{t}, @var{df}] =} t_test_2 (@var{x}, @var{y}, @var{alt}) |
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22 ## For two samples x and y from normal distributions with unknown means |
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23 ## and unknown equal variances, perform a two-sample t-test of the null |
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24 ## hypothesis of equal means. Under the null, the test statistic |
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25 ## @var{t} follows a Student distribution with @var{df} degrees of |
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26 ## freedom. |
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27 ## |
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28 ## With the optional argument string @var{alt}, the alternative of |
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29 ## interest can be selected. If @var{alt} is @code{"!="} or |
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30 ## @code{"<>"}, the null is tested against the two-sided alternative |
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31 ## @code{mean (@var{x}) != mean (@var{y})}. If @var{alt} is @code{">"}, |
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32 ## the one-sided alternative @code{mean (@var{x}) > mean (@var{y})} is |
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33 ## used. Similarly for @code{"<"}, the one-sided alternative @code{mean |
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34 ## (@var{x}) < mean (@var{y})} is used. The default is the two-sided |
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35 ## case. |
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36 ## |
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37 ## The p-value of the test is returned in @var{pval}. |
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38 ## |
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39 ## If no output argument is given, the p-value of the test is displayed. |
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40 ## @end deftypefn |
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41 |
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42 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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43 ## Description: Student's two-sample t test |
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44 |
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45 function [pval, t, df] = t_test_2 (x, y, alt) |
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46 |
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47 if ((nargin < 2) || (nargin > 3)) |
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48 print_usage (); |
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49 endif |
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50 |
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51 if (! (isvector (x) && isvector (y))) |
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52 error ("t_test_2: both x and y must be vectors"); |
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53 endif |
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54 |
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55 n_x = length (x); |
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56 n_y = length (y); |
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57 df = n_x + n_y - 2; |
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58 mu_x = sum (x) / n_x; |
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59 mu_y = sum (y) / n_y; |
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60 v = sumsq (x - mu_x) + sumsq (y - mu_y); |
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61 t = (mu_x - mu_y) * sqrt ((n_x * n_y * df) / (v * (n_x + n_y))); |
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62 cdf = t_cdf (t, df); |
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63 |
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64 if (nargin == 2) |
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65 alt = "!="; |
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66 endif |
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67 |
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68 if (! ischar (alt)) |
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69 error ("t_test_2: alt must be a string"); |
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70 endif |
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71 if (strcmp (alt, "!=") || strcmp (alt, "<>")) |
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72 pval = 2 * min (cdf, 1 - cdf); |
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73 elseif strcmp (alt, ">") |
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74 pval = 1 - cdf; |
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75 elseif strcmp (alt, "<") |
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76 pval = cdf; |
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77 else |
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78 error ("t_test_2: option %s not recognized", alt); |
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79 endif |
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80 |
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81 if (nargout == 0) |
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82 printf (" pval: %g\n", pval); |
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83 endif |
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84 |
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85 endfunction |
