1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
|
## Copyright (C) 1995, 1996, 1997 Kurt Hornik
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
##
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this file. If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
## usage: cor_test (X, Y [, ALTERNATIVE [, METHOD]])
##
## Test whether two samples X and Y come from uncorrelated populations.
##
## The optional argument string ALTERNATIVE describes the alternative
## hypothesis, and can be "!=" or "<>" (non-zero), ">" (greater than 0),
## or "<" (less than 0). The default is the two-sided case.
##
## The optional argument string METHOD specifies on which correlation
## coefficient the test should be based.
## If METHOD is "pearson" (default), the (usual) Pearson's product
## moment correlation coefficient is used. In this case, the data
## should come from a bivariate normal distribution. Otherwise, the
## other two methods offer nonparametric alternatives.
## If METHOD is "kendall", then Kendall's rank correlation tau is used.
## If METHOD is "spearman", then Spearman's rank correlation rho is used.
## Only the first character is necessary.
##
## The output is a structure with the following elements:
## pval The p-value of the test.
## stat The value of the test statistic.
## dist The distribution of the test statistic.
## params The parameters of the null distribution of the
## test statistic.
## alternative The alternative hypothesis.
## method The method used for testing.
##
## If no output argument is given, the pval is displayed.
## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at>
## Adapted-by: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description: Test for zero correlation
function t = cor_test (X, Y, ALTERNATIVE, METHOD)
if ((nargin < 2) || (nargin > 4))
usage ("cor_test (X, Y [, ALTERNATIVE [, METHOD]])")
endif
if (!is_vector (X) || !is_vector (Y) || length (X) != length (Y))
error ("cor_test: X and Y must be vectors of the same length")
endif
if (nargin < 3)
ALTERNATIVE = "!=";
elseif !isstr (ALTERNATIVE)
error ("cor_test: ALTERNATIVE must be a string");
endif
if (nargin < 4)
METHOD = "pearson";
elseif !isstr (METHOD)
error ("cor_test: METHOD must be a string");
endif
n = length (X);
m = METHOD (1);
if (m == "p")
r = cor (X, Y);
df = n - 2;
t.method = "Pearson's product moment correlation";
t.params = df;
t.stat = sqrt (df) .* r / sqrt (1 - r.^2);
t.dist = "t";
cdf = t_cdf (t.stat, df);
elseif (m == "k")
tau = kendall (X, Y);
t.method = "Kendall's rank correlation tau";
t.params = [];
t.stat = tau / sqrt ((2 * (2*n+5)) / (9*n*(n-1)));
t.dist = "stdnormal";
cdf = stdnormal_cdf (t.stat);
elseif (m == "s")
rho = spearman (X, Y);
t.method = "Spearman's rank correlation rho";
t.params = [];
t.stat = sqrt (n-1) * (rho - 6/(n^3-n));
t.dist = "stdnormal";
cdf = stdnormal_cdf (t.stat);
else
error ("cor_test: method `%s' not recognized", METHOD)
endif
if (strcmp (ALTERNATIVE, "!=") || strcmp (ALTERNATIVE, "<>"))
t.pval = 2 * min (cdf, 1 - cdf);
elseif (strcmp (ALTERNATIVE, ">"))
t.pval = 1 - cdf;
elseif (strcmp (ALTERNATIVE, "<"))
t.pval = cdf;
else
error ("cor_test: alternative `%s' not recognized", ALTERNATIVE);
endif
t.alternative = ALTERNATIVE;
if (nargout == 0)
printf ("pval: %g\n", t.pval);
endif
endfunction
|
