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1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik |
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2 ## |
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3 ## This program is free software; you can redistribute it and/or modify |
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4 ## it under the terms of the GNU General Public License as published by |
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5 ## the Free Software Foundation; either version 2, or (at your option) |
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6 ## any later version. |
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7 ## |
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8 ## This program is distributed in the hope that it will be useful, but |
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9 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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11 ## General Public License for more details. |
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12 ## |
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13 ## You should have received a copy of the GNU General Public License |
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14 ## along with this file. If not, write to the Free Software Foundation, |
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15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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16 |
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17 ## -*- texinfo -*- |
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18 ## @deftypefn {Function File} {[@var{pval}, @var{t}, @var{df}] =} welch_test (@var{x}, @var{y}, @var{alt}) |
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19 ## For two samples @var{x} and @var{y} from normal distributions with |
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20 ## unknown means and unknown and not necessarily equal variances, |
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21 ## perform a Welch test of the null hypothesis of equal means. |
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22 ## Under the null, the test statistic t approximately follows a Student |
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23 ## distribution with df degrees of freedom. |
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24 ## |
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25 ## With the optional argument string @var{alt}, the alternative of |
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26 ## interest can be selected. If @var{alt} is @code{"!="} or |
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27 ## @code{"<>"}, the null is tested against the two-sided alternative |
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28 ## @code{mean (@var{x}) != @var{m}}. If @var{alt} is @code{">"}, the |
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29 ## one-sided alternative mean(x) > @var{m} is considered. Similarly for |
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30 ## @code{"<"}, the one-sided alternative mean(x) < @var{m} is |
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31 ## considered. The default is the two-sided case. |
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32 ## |
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33 ## The p-value of the test is returned in @var{pval}. |
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34 ## |
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35 ## If no output argument is given, the p-value of the test is displayed. |
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36 ## @end deftypefn |
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37 |
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38 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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39 ## Description: Welch two-sample t test |
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40 |
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41 function [pval, t, df] = welch_test (x, y, alt) |
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42 |
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43 if ((nargin < 2) || (nargin > 3)) |
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44 usage ("[pval, t, df] = welch_test (x, y, alt)"); |
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45 endif |
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46 |
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47 if (! (is_vector (x) && is_vector (y))) |
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48 error ("welch_test: both x and y must be vectors"); |
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49 endif |
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50 |
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51 n_x = length (x); |
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52 n_y = length (y); |
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53 mu_x = sum (x) / n_x; |
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54 mu_y = sum (y) / n_y; |
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55 v_x = sumsq (x - mu_x) / (n_x * (n_x - 1)); |
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56 v_y = sumsq (x - mu_y) / (n_y * (n_y - 1)); |
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57 c = v_x / (v_x + v_y); |
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58 df = 1 / (c^2 / (n_x - 1) + (1 - c)^2 / (n_y - 1)); |
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59 t = (mu_x - mu_y) / sqrt (v_x + v_y); |
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60 cdf = t_cdf (t, df); |
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61 |
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62 if (nargin == 2) |
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63 alt = "!="; |
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64 endif |
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65 |
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66 if (! isstr (alt)) |
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67 error ("welch_test: alt must be a string"); |
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68 endif |
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69 if (strcmp (alt, "!=") || strcmp (alt, "<>")) |
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70 pval = 2 * min (cdf, 1 - cdf); |
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71 elseif (strcmp (alt, ">")) |
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72 pval = 1 - cdf; |
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73 elseif (strcmp (alt, "<")) |
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74 pval = cdf; |
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75 else |
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76 error ("welch_test: option %s not recognized", alt); |
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77 endif |
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78 |
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79 if (nargout == 0) |
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80 printf (" pval: %g\n", pval); |
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81 endif |
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82 |
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83 endfunction |
