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
118
119
120
121
122
123
124
125
|
########################################################################
##
## Copyright (C) 1995-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## This file is part of Octave.
##
## Octave 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 3 of the License, or
## (at your option) any later version.
##
## Octave 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 Octave; see the file COPYING. If not, see
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {@var{rho} =} spearman (@var{x})
## @deftypefnx {} {@var{rho} =} spearman (@var{x}, @var{y})
## @cindex Spearman's Rho
## Compute Spearman's rank correlation coefficient
## @tex
## $\rho$.
## @end tex
## @ifnottex
## @var{rho}.
## @end ifnottex
##
## For two data vectors @var{x} and @var{y}, Spearman's
## @tex
## $\rho$
## @end tex
## @ifnottex
## @var{rho}
## @end ifnottex
## is the correlation coefficient of the ranks of @var{x} and @var{y}.
##
## If @var{x} and @var{y} are drawn from independent distributions,
## @tex
## $\rho$
## @end tex
## @ifnottex
## @var{rho}
## @end ifnottex
## has zero mean and variance
## @tex
## $1 / (N - 1)$,
## @end tex
## @ifnottex
## @code{1 / (N - 1)},
## @end ifnottex
## where @math{N} is the length of the @var{x} and @var{y} vectors, and is
## asymptotically normally distributed.
##
## @code{spearman (@var{x})} is equivalent to
## @code{spearman (@var{x}, @var{x})}.
## @seealso{ranks, kendall}
## @end deftypefn
function rho = spearman (x, y = [])
if (nargin < 1)
print_usage ();
endif
if ( ! (isnumeric (x) || islogical (x))
|| ! (isnumeric (y) || islogical (y)))
error ("spearman: X and Y must be numeric matrices or vectors");
endif
if (ndims (x) != 2 || ndims (y) != 2)
error ("spearman: X and Y must be 2-D matrices or vectors");
endif
if (isrow (x))
x = x.';
endif
if (nargin == 1)
rho = corr (ranks (x));
else
if (isrow (y))
y = y.';
endif
if (rows (x) != rows (y))
error ("spearman: X and Y must have the same number of observations");
endif
rho = corr (ranks (x), ranks (y));
endif
## Restore class cleared by ranks
if (isa (x, "single") || isa (y, "single"))
rho = single (rho);
endif
endfunction
%!test
%! x = 1:10;
%! y = exp (x);
%! assert (spearman (x,y), 1, 5*eps);
%! assert (spearman (x,-y), -1, 5*eps);
%!assert (spearman ([1 2 3], [-1 1 -2]), -0.5, 5*eps)
%!assert (spearman (1), NaN)
%!assert (spearman (single (1)), single (NaN))
## Test input validation
%!error <Invalid call> spearman ()
%!error spearman (['A'; 'B'])
%!error spearman (ones (1,2), {1, 2})
%!error spearman (ones (2,2,2))
%!error spearman (ones (2,2), ones (2,2,2))
%!error spearman (ones (2,2), ones (3,2))
|
