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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 ## usage: cor_test (X, Y [, ALTERNATIVE [, METHOD]]) |
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18 ## |
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19 ## Test whether two samples X and Y come from uncorrelated populations. |
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20 ## |
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21 ## The optional argument string ALTERNATIVE describes the alternative |
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22 ## hypothesis, and can be "!=" or "<>" (non-zero), ">" (greater than 0), |
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23 ## or "<" (less than 0). The default is the two-sided case. |
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24 ## |
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25 ## The optional argument string METHOD specifies on which correlation |
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26 ## coefficient the test should be based. |
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27 ## If METHOD is "pearson" (default), the (usual) Pearson's product |
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28 ## moment correlation coefficient is used. In this case, the data |
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29 ## should come from a bivariate normal distribution. Otherwise, the |
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30 ## other two methods offer nonparametric alternatives. |
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31 ## If METHOD is "kendall", then Kendall's rank correlation tau is used. |
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32 ## If METHOD is "spearman", then Spearman's rank correlation rho is used. |
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33 ## Only the first character is necessary. |
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34 ## |
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35 ## The output is a structure with the following elements: |
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36 ## pval The p-value of the test. |
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37 ## stat The value of the test statistic. |
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38 ## dist The distribution of the test statistic. |
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39 ## params The parameters of the null distribution of the |
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40 ## test statistic. |
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41 ## alternative The alternative hypothesis. |
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42 ## method The method used for testing. |
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43 ## |
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44 ## If no output argument is given, the pval is displayed. |
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45 |
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46 ## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at> |
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47 ## Adapted-by: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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48 ## Description: Test for zero correlation |
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49 |
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50 function t = cor_test (X, Y, ALTERNATIVE, METHOD) |
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51 |
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52 if ((nargin < 2) || (nargin > 4)) |
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53 usage ("cor_test (X, Y [, ALTERNATIVE [, METHOD]])") |
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54 endif |
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55 |
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56 if (!is_vector (X) || !is_vector (Y) || length (X) != length (Y)) |
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57 error ("cor_test: X and Y must be vectors of the same length") |
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58 endif |
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59 |
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60 if (nargin < 3) |
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61 ALTERNATIVE = "!="; |
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62 elseif !isstr (ALTERNATIVE) |
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63 error ("cor_test: ALTERNATIVE must be a string"); |
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64 endif |
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65 |
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66 if (nargin < 4) |
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67 METHOD = "pearson"; |
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68 elseif !isstr (METHOD) |
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69 error ("cor_test: METHOD must be a string"); |
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70 endif |
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71 |
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72 n = length (X); |
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73 m = METHOD (1); |
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74 |
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75 if (m == "p") |
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76 r = cor (X, Y); |
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77 df = n - 2; |
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78 t.method = "Pearson's product moment correlation"; |
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79 t.params = df; |
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80 t.stat = sqrt (df) .* r / sqrt (1 - r.^2); |
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81 t.dist = "t"; |
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82 cdf = t_cdf (t.stat, df); |
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83 elseif (m == "k") |
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84 tau = kendall (X, Y); |
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85 t.method = "Kendall's rank correlation tau"; |
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86 t.params = []; |
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87 t.stat = tau / sqrt ((2 * (2*n+5)) / (9*n*(n-1))); |
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88 t.dist = "stdnormal"; |
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89 cdf = stdnormal_cdf (t.stat); |
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90 elseif (m == "s") |
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91 rho = spearman (X, Y); |
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92 t.method = "Spearman's rank correlation rho"; |
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93 t.params = []; |
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94 t.stat = sqrt (n-1) * (rho - 6/(n^3-n)); |
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95 t.dist = "stdnormal"; |
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96 cdf = stdnormal_cdf (t.stat); |
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97 else |
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98 error ("cor_test: method `%s' not recognized", METHOD) |
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99 endif |
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100 |
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101 if (strcmp (ALTERNATIVE, "!=") || strcmp (ALTERNATIVE, "<>")) |
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102 t.pval = 2 * min (cdf, 1 - cdf); |
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103 elseif (strcmp (ALTERNATIVE, ">")) |
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104 t.pval = 1 - cdf; |
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105 elseif (strcmp (ALTERNATIVE, "<")) |
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106 t.pval = cdf; |
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107 else |
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108 error ("cor_test: alternative `%s' not recognized", ALTERNATIVE); |
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109 endif |
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110 |
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111 t.alternative = ALTERNATIVE; |
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112 |
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113 if (nargout == 0) |
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114 printf ("pval: %g\n", t.pval); |
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115 endif |
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116 |
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117 endfunction |
