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1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 2, or (at your option) |
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8 ## any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, write to the Free |
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17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301, USA. |
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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 (@var{x}, @var{m}, @var{alt}) |
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22 ## For a sample @var{x} from a normal distribution with unknown mean and |
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23 ## variance, perform a t-test of the null hypothesis @code{mean |
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24 ## (@var{x}) == @var{m}}. Under the null, the test statistic @var{t} |
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25 ## follows a Student distribution with @code{@var{df} = length (@var{x}) |
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26 ## - 1} degrees of 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}) != @var{m}}. If @var{alt} is @code{">"}, the |
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32 ## one-sided alternative @code{mean (@var{x}) > @var{m}} is considered. |
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33 ## Similarly for @var{"<"}, the one-sided alternative @code{mean |
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34 ## (@var{x}) < @var{m}} is considered, 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 one-sample t test |
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44 |
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45 function [pval, t, df] = t_test (x, m, alt) |
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46 |
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47 if ((nargin < 2) || (nargin > 3)) |
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48 usage ("[pval, t, df] = t_test (x, m, alt)"); |
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49 endif |
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50 |
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51 if (! isvector (x)) |
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52 error ("t_test: x must be a vector"); |
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53 endif |
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54 if (! isscalar (m)) |
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55 error ("t_test: m must be a scalar"); |
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56 endif |
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57 |
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58 n = length (x); |
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59 df = n - 1; |
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60 t = sqrt (n) * (sum (x) / n - m) / std (x); |
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61 cdf = t_cdf (t, df); |
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62 |
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63 if (nargin == 2) |
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64 alt = "!="; |
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65 endif |
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66 |
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67 if (! isstr (alt)) |
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68 error ("t_test: alt must be a string"); |
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69 endif |
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70 if (strcmp (alt, "!=") || strcmp (alt, "<>")) |
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71 pval = 2 * min (cdf, 1 - cdf); |
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72 elseif strcmp (alt, ">") |
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73 pval = 1 - cdf; |
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74 elseif strcmp (alt, "<") |
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75 pval = cdf; |
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76 else |
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77 error ("t_test: option %s not recognized", alt); |
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78 endif |
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79 |
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80 if (nargout == 0) |
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81 printf (" pval: %g\n", pval); |
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82 endif |
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83 |
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84 endfunction |
