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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} {} cor_test (@var{x}, @var{y}, @var{alt}, @var{method}) |
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22 ## Test whether two samples @var{x} and @var{y} come from uncorrelated |
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23 ## populations. |
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24 ## |
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25 ## The optional argument string @var{alt} describes the alternative |
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26 ## hypothesis, and can be @code{"!="} or @code{"<>"} (non-zero), |
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27 ## @code{">"} (greater than 0), or @code{"<"} (less than 0). The |
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28 ## default is the two-sided case. |
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29 ## |
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30 ## The optional argument string @var{method} specifies on which |
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31 ## correlation coefficient the test should be based. If @var{method} is |
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32 ## @code{"pearson"} (default), the (usual) Pearson's product moment |
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33 ## correlation coefficient is used. In this case, the data should come |
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34 ## from a bivariate normal distribution. Otherwise, the other two |
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35 ## methods offer nonparametric alternatives. If @var{method} is |
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36 ## @code{"kendall"}, then Kendall's rank correlation tau is used. If |
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37 ## @var{method} is @code{"spearman"}, then Spearman's rank correlation |
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38 ## rho is used. Only the first character is necessary. |
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39 ## |
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40 ## The output is a structure with the following elements: |
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41 ## |
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42 ## @table @var |
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43 ## @item pval |
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44 ## The p-value of the test. |
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45 ## @item stat |
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46 ## The value of the test statistic. |
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47 ## @item dist |
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48 ## The distribution of the test statistic. |
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49 ## @item params |
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50 ## The parameters of the null distribution of the test statistic. |
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51 ## @item alternative |
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52 ## The alternative hypothesis. |
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53 ## @item method |
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54 ## The method used for testing. |
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55 ## @end table |
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56 ## |
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57 ## If no output argument is given, the p-value is displayed. |
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58 ## @end deftypefn |
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59 |
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60 ## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at> |
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61 ## Adapted-by: KH <Kurt.Hornik@wu-wien.ac.at> |
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62 ## Description: Test for zero correlation |
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63 |
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64 function t = cor_test (X, Y, ALTERNATIVE, METHOD) |
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65 |
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66 if ((nargin < 2) || (nargin > 4)) |
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67 print_usage (); |
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68 endif |
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69 |
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70 if (!isvector (X) || !isvector (Y) || length (X) != length (Y)) |
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71 error ("cor_test: X and Y must be vectors of the same length"); |
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72 endif |
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73 |
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74 if (nargin < 3) |
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75 ALTERNATIVE = "!="; |
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76 elseif (! ischar (ALTERNATIVE)) |
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77 error ("cor_test: ALTERNATIVE must be a string"); |
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78 endif |
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79 |
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80 if (nargin < 4) |
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81 METHOD = "pearson"; |
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82 elseif (! ischar (METHOD)) |
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83 error ("cor_test: METHOD must be a string"); |
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84 endif |
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85 |
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86 n = length (X); |
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87 m = METHOD (1); |
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88 |
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89 if (m == "p") |
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90 r = cor (X, Y); |
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91 df = n - 2; |
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92 t.method = "Pearson's product moment correlation"; |
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93 t.params = df; |
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94 t.stat = sqrt (df) .* r / sqrt (1 - r.^2); |
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95 t.dist = "t"; |
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96 cdf = t_cdf (t.stat, df); |
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97 elseif (m == "k") |
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98 tau = kendall (X, Y); |
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99 t.method = "Kendall's rank correlation tau"; |
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100 t.params = []; |
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101 t.stat = tau / sqrt ((2 * (2*n+5)) / (9*n*(n-1))); |
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102 t.dist = "stdnormal"; |
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103 cdf = stdnormal_cdf (t.stat); |
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104 elseif (m == "s") |
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105 rho = spearman (X, Y); |
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106 t.method = "Spearman's rank correlation rho"; |
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107 t.params = []; |
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108 t.stat = sqrt (n-1) * (rho - 6/(n^3-n)); |
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109 t.dist = "stdnormal"; |
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110 cdf = stdnormal_cdf (t.stat); |
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111 else |
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112 error ("cor_test: method `%s' not recognized", METHOD); |
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113 endif |
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114 |
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115 if (strcmp (ALTERNATIVE, "!=") || strcmp (ALTERNATIVE, "<>")) |
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116 t.pval = 2 * min (cdf, 1 - cdf); |
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117 elseif (strcmp (ALTERNATIVE, ">")) |
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118 t.pval = 1 - cdf; |
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119 elseif (strcmp (ALTERNATIVE, "<")) |
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120 t.pval = cdf; |
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121 else |
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122 error ("cor_test: alternative `%s' not recognized", ALTERNATIVE); |
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123 endif |
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124 |
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125 t.alternative = ALTERNATIVE; |
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126 |
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127 if (nargout == 0) |
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128 printf ("pval: %g\n", t.pval); |
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129 endif |
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130 |
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131 endfunction |
