Mercurial > hg > octave-nkf
annotate scripts/statistics/tests/cor_test.m @ 20818:9d2023d1a63c
binoinv.m: Implement binary search algorithm for 28X performance increase (bug #34363).
* binoinv.m: Call new functions scalar_binoinv or vector_binoinv to calculate
binoinv. If there are still uncalculated values then call bin_search_binoinv
to perform binary search for remaining values. Add more BIST tests.
* binoinv.m (scalar_binoinv): New subfunction to calculate binoinv for scalar x.
Stops when x > 1000.
* binoinv.m (vector_binoinv): New subfunction to calculate binoinv for scalar x.
Stops when x > 1000.
| author | Lachlan Andrew <lachlanbis@gmail.com> |
|---|---|
| date | Sun, 11 Oct 2015 19:49:40 -0700 |
| parents | d9341b422488 |
| children |
| rev | line source |
|---|---|
|
19898
4197fc428c7d
maint: Update copyright notices for 2015.
John W. Eaton <jwe@octave.org>
parents:
19007
diff
changeset
|
1 ## Copyright (C) 1995-2015 Kurt Hornik |
| 3426 | 2 ## |
| 3922 | 3 ## This file is part of Octave. |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 3426 | 9 ## |
| 3922 | 10 ## Octave is distributed in the hope that it will be useful, but |
| 3200 | 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 3426 | 13 ## General Public License for more details. |
| 14 ## | |
| 3200 | 15 ## You should have received a copy of the GNU General Public License |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 3200 | 18 |
| 3454 | 19 ## -*- texinfo -*- |
| 20 ## @deftypefn {Function File} {} cor_test (@var{x}, @var{y}, @var{alt}, @var{method}) | |
| 21 ## Test whether two samples @var{x} and @var{y} come from uncorrelated | |
| 22 ## populations. | |
| 3200 | 23 ## |
| 3454 | 24 ## The optional argument string @var{alt} describes the alternative |
|
20384
d9341b422488
doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents:
20038
diff
changeset
|
25 ## hypothesis, and can be @qcode{"!="} or @qcode{"<>"} (nonzero), @qcode{">"} |
|
d9341b422488
doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents:
20038
diff
changeset
|
26 ## (greater than 0), or @qcode{"<"} (less than 0). The default is the |
|
d9341b422488
doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents:
20038
diff
changeset
|
27 ## two-sided case. |
| 3200 | 28 ## |
|
20384
d9341b422488
doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents:
20038
diff
changeset
|
29 ## The optional argument string @var{method} specifies which correlation |
|
d9341b422488
doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents:
20038
diff
changeset
|
30 ## coefficient to use for testing. If @var{method} is @qcode{"pearson"} |
|
d9341b422488
doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents:
20038
diff
changeset
|
31 ## (default), the (usual) Pearson's produt moment correlation coefficient is |
|
d9341b422488
doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents:
20038
diff
changeset
|
32 ## used. In this case, the data should come from a bivariate normal |
|
d9341b422488
doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents:
20038
diff
changeset
|
33 ## distribution. Otherwise, the other two methods offer nonparametric |
|
d9341b422488
doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents:
20038
diff
changeset
|
34 ## alternatives. If @var{method} is @qcode{"kendall"}, then Kendall's rank |
|
d9341b422488
doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents:
20038
diff
changeset
|
35 ## correlation tau is used. If @var{method} is @qcode{"spearman"}, then |
|
d9341b422488
doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents:
20038
diff
changeset
|
36 ## Spearman's rank correlation rho is used. Only the first character is |
|
d9341b422488
doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents:
20038
diff
changeset
|
37 ## necessary. |
| 3200 | 38 ## |
| 39 ## The output is a structure with the following elements: | |
| 40 ## | |
| 3454 | 41 ## @table @var |
| 42 ## @item pval | |
| 43 ## The p-value of the test. | |
|
10821
693e22af08ae
Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents:
10606
diff
changeset
|
44 ## |
| 3454 | 45 ## @item stat |
| 46 ## The value of the test statistic. | |
|
10821
693e22af08ae
Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents:
10606
diff
changeset
|
47 ## |
| 3454 | 48 ## @item dist |
| 49 ## The distribution of the test statistic. | |
|
10821
693e22af08ae
Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents:
10606
diff
changeset
|
50 ## |
| 3454 | 51 ## @item params |
| 52 ## The parameters of the null distribution of the test statistic. | |
|
10821
693e22af08ae
Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents:
10606
diff
changeset
|
53 ## |
| 3454 | 54 ## @item alternative |
| 55 ## The alternative hypothesis. | |
|
10821
693e22af08ae
Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents:
10606
diff
changeset
|
56 ## |
| 3454 | 57 ## @item method |
| 58 ## The method used for testing. | |
| 59 ## @end table | |
| 60 ## | |
| 61 ## If no output argument is given, the p-value is displayed. | |
| 62 ## @end deftypefn | |
| 3200 | 63 |
| 3456 | 64 ## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at> |
| 5428 | 65 ## Adapted-by: KH <Kurt.Hornik@wu-wien.ac.at> |
| 3456 | 66 ## Description: Test for zero correlation |
| 3200 | 67 |
|
11469
c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
10821
diff
changeset
|
68 function t = cor_test (x, y, alt, method) |
| 3426 | 69 |
|
20038
9fc020886ae9
maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents:
19898
diff
changeset
|
70 if (nargin < 2 || nargin > 4) |
| 6046 | 71 print_usage (); |
| 3200 | 72 endif |
| 73 | |
|
20038
9fc020886ae9
maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents:
19898
diff
changeset
|
74 if (! isvector (x) || ! isvector (y) || length (x) != length (y)) |
| 8664 | 75 error ("cor_test: X and Y must be vectors of the same length"); |
| 3200 | 76 endif |
| 77 | |
| 78 if (nargin < 3) | |
|
11469
c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
10821
diff
changeset
|
79 alt = "!="; |
|
c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
10821
diff
changeset
|
80 elseif (! ischar (alt)) |
|
11472
1740012184f9
Use uppercase for variable names in error() strings to match Info documentation. Only m-files done.
Rik <octave@nomad.inbox5.com>
parents:
11469
diff
changeset
|
81 error ("cor_test: ALT must be a string"); |
| 3200 | 82 endif |
| 83 | |
| 84 if (nargin < 4) | |
|
11469
c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
10821
diff
changeset
|
85 method = "pearson"; |
|
c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
10821
diff
changeset
|
86 elseif (! ischar (method)) |
| 3456 | 87 error ("cor_test: METHOD must be a string"); |
| 3200 | 88 endif |
| 89 | |
|
11469
c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
10821
diff
changeset
|
90 n = length (x); |
|
20038
9fc020886ae9
maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents:
19898
diff
changeset
|
91 m = method(1); |
| 3200 | 92 |
| 93 if (m == "p") | |
|
12856
cad4cba03f19
Deprecate corrcoef, cor and replace with Matlab equivalent corr
Rik <octave@nomad.inbox5.com>
parents:
12480
diff
changeset
|
94 r = corr (x, y); |
| 3200 | 95 df = n - 2; |
| 96 t.method = "Pearson's product moment correlation"; | |
| 97 t.params = df; | |
| 98 t.stat = sqrt (df) .* r / sqrt (1 - r.^2); | |
| 99 t.dist = "t"; | |
|
20038
9fc020886ae9
maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents:
19898
diff
changeset
|
100 cdf = tcdf (t.stat, df); |
| 3200 | 101 elseif (m == "k") |
|
11469
c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
10821
diff
changeset
|
102 tau = kendall (x, y); |
| 3426 | 103 t.method = "Kendall's rank correlation tau"; |
| 3200 | 104 t.params = []; |
| 105 t.stat = tau / sqrt ((2 * (2*n+5)) / (9*n*(n-1))); | |
| 106 t.dist = "stdnormal"; | |
| 107 cdf = stdnormal_cdf (t.stat); | |
| 108 elseif (m == "s") | |
|
11469
c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
10821
diff
changeset
|
109 rho = spearman (x, y); |
| 3200 | 110 t.method = "Spearman's rank correlation rho"; |
| 111 t.params = []; | |
| 112 t.stat = sqrt (n-1) * (rho - 6/(n^3-n)); | |
| 3426 | 113 t.dist = "stdnormal"; |
| 3200 | 114 cdf = stdnormal_cdf (t.stat); |
| 115 else | |
|
15466
d174210ce1ec
use ' instead of ` in error messages, warnings and most comments
John W. Eaton <jwe@octave.org>
parents:
14138
diff
changeset
|
116 error ("cor_test: METHOD '%s' not recognized", method); |
| 3200 | 117 endif |
| 118 | |
|
11469
c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
10821
diff
changeset
|
119 if (strcmp (alt, "!=") || strcmp (alt, "<>")) |
| 3200 | 120 t.pval = 2 * min (cdf, 1 - cdf); |
|
11469
c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
10821
diff
changeset
|
121 elseif (strcmp (alt, ">")) |
| 3200 | 122 t.pval = 1 - cdf; |
|
11469
c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
10821
diff
changeset
|
123 elseif (strcmp (alt, "<")) |
| 3200 | 124 t.pval = cdf; |
| 125 else | |
|
15466
d174210ce1ec
use ' instead of ` in error messages, warnings and most comments
John W. Eaton <jwe@octave.org>
parents:
14138
diff
changeset
|
126 error ("cor_test: alternative '%s' not recognized", alt); |
| 3200 | 127 endif |
| 128 | |
|
11469
c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
10821
diff
changeset
|
129 t.alternative = alt; |
| 3200 | 130 |
| 131 if (nargout == 0) | |
| 3456 | 132 printf ("pval: %g\n", t.pval); |
| 3200 | 133 endif |
| 3426 | 134 |
| 3200 | 135 endfunction |
|
17338
1c89599167a6
maint: End m-files with 1 blank line.
Rik <rik@octave.org>
parents:
17281
diff
changeset
|
136 |