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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 3 of the License, or (at |
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8 ## your option) 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, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {[@var{pval}, @var{z}] =} z_test_2 (@var{x}, @var{y}, @var{v_x}, @var{v_y}, @var{alt}) |
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21 ## For two samples @var{x} and @var{y} from normal distributions with |
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22 ## unknown means and known variances @var{v_x} and @var{v_y}, perform a |
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23 ## Z-test of the hypothesis of equal means. Under the null, the test |
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24 ## statistic @var{z} follows a standard normal distribution. |
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25 ## |
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26 ## With the optional argument string @var{alt}, the alternative of |
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27 ## interest can be selected. If @var{alt} is @code{"!="} or |
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28 ## @code{"<>"}, the null is tested against the two-sided alternative |
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29 ## @code{mean (@var{x}) != mean (@var{y})}. If alt is @code{">"}, the |
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30 ## one-sided alternative @code{mean (@var{x}) > mean (@var{y})} is used. |
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31 ## Similarly for @code{"<"}, the one-sided alternative @code{mean |
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32 ## (@var{x}) < mean (@var{y})} is used. The default is the two-sided |
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33 ## case. |
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34 ## |
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35 ## The p-value of the test is returned in @var{pval}. |
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36 ## |
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37 ## If no output argument is given, the p-value of the test is displayed |
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38 ## along with some information. |
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39 ## @end deftypefn |
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40 |
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41 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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42 ## Description: Compare means of two normal samples with known variances |
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43 |
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44 function [pval, z] = z_test_2 (x, y, v_x, v_y, alt) |
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45 |
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46 if ((nargin < 4) || (nargin > 5)) |
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47 print_usage (); |
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48 endif |
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49 |
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50 if (! (isvector (x) && isvector (y))) |
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51 error("z_test_2: both x and y must be vectors"); |
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52 elseif (! (isscalar (v_x) && (v_x > 0) |
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53 && isscalar (v_y) && (v_y > 0))) |
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54 error ("z_test_2: both v_x and v_y must be positive scalars"); |
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55 endif |
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56 |
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57 n_x = length (x); |
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58 n_y = length (y); |
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59 mu_x = sum (x) / n_x; |
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60 mu_y = sum (y) / n_y; |
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61 z = (mu_x - mu_y) / sqrt (v_x / n_x + v_y / n_y); |
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62 cdf = stdnormal_cdf (z); |
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63 |
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64 if (nargin == 4) |
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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 ("z_test_2: alt must be a string"); |
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70 elseif (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 ("z_test_2: 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 s = strcat ("Two-sample Z-test of mean(x) == mean(y) against ", |
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82 "mean(x) %s mean(y),\n", |
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83 "with known var(x) == %g and var(y) == %g:\n", |
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84 " pval = %g\n"); |
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85 printf (s, alt, v_x, v_y, pval); |
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86 endif |
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87 |
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88 endfunction |
