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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{z}] =} z_test (@var{x}, @var{m}, @var{v}, @var{alt}) |
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19 ## Perform a Z-test of the null hypothesis @code{mean (@var{x}) == |
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20 ## @var{m}} for a sample @var{x} from a normal distribution with unknown |
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21 ## mean and known variance @var{v}. Under the null, the test statistic |
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22 ## @var{z} follows a standard normal distribution. |
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23 ## |
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24 ## With the optional argument string @var{alt}, the alternative of |
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25 ## interest can be selected. If @var{alt} is @code{"!="} or |
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26 ## @code{"<>"}, the null is tested against the two-sided alternative |
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27 ## @code{mean (@var{x}) != @var{m}}. If @var{alt} is @code{">"}, the |
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28 ## one-sided alternative @code{mean (@var{x}) > @var{m}} is considered. |
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29 ## Similarly for @code{"<"}, the one-sided alternative @code{mean |
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30 ## (@var{x}) < @var{m}} is considered. The default is the two-sided |
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31 ## 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 ## along with some information. |
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37 ## @end deftypefn |
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38 |
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39 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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40 ## Description: Test for mean of a normal sample with known variance |
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41 |
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42 function [pval, z] = z_test (x, m, v, alt) |
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43 |
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44 if ((nargin < 3) || (nargin > 4)) |
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45 usage ("[pval, z] = z_test (x, m, v, alt)"); |
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46 endif |
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47 |
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48 if (! is_vector (x)) |
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49 error ("z_test: x must be a vector."); |
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50 endif |
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51 if (! is_scalar (m)) |
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52 error ("z_test: m must be a scalar."); |
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53 endif |
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54 if (! (is_scalar (v) && (v > 0))) |
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55 error ("z_test: v must be a positive 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 z = sqrt (n/v) * (sum (x) / n - m); |
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60 cdf = stdnormal_cdf (z); |
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61 |
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62 if (nargin == 3) |
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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 ("z_test: alt must be a string"); |
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68 elseif (strcmp (alt, "!=") || strcmp (alt, "<>")) |
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69 pval = 2 * min (cdf, 1 - cdf); |
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70 elseif (strcmp (alt, ">")) |
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71 pval = 1 - cdf; |
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72 elseif (strcmp (alt, "<")) |
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73 pval = cdf; |
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74 else |
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75 error ("z_test: option %s not recognized", alt); |
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76 endif |
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77 |
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78 if (nargout == 0) |
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79 s = strcat ("Z-test of mean(x) == %g against mean(x) %s %g,\n", |
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80 "with known var(x) == %g:\n", |
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81 " pval = %g\n"); |
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82 printf (s, m, alt, m, v, pval); |
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83 endif |
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84 |
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85 endfunction |
