|
3200
|
1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik |
|
3426
|
2 ## |
|
3200
|
3 ## This program is free software; you can redistribute it and/or modify |
|
|
4 ## it under the terms of the GNU General Public License as published by |
|
|
5 ## the Free Software Foundation; either version 2, or (at your option) |
|
|
6 ## any later version. |
|
3426
|
7 ## |
|
3200
|
8 ## This program is distributed in the hope that it will be useful, but |
|
|
9 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
|
|
10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
|
3426
|
11 ## General Public License for more details. |
|
|
12 ## |
|
3200
|
13 ## You should have received a copy of the GNU General Public License |
|
|
14 ## along with this file. If not, write to the Free Software Foundation, |
|
|
15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
|
|
16 |
|
|
17 ## usage: [pval, t, df] = t_test_2 (x, y [, alt]) |
|
|
18 ## |
|
|
19 ## For two samples x and y from normal distributions with unknown means |
|
|
20 ## and unknown equal variances, perform a two-sample t-test of the null |
|
|
21 ## hypothesis of equal means. |
|
|
22 ## Under the null, the test statistic t follows a Student distribution |
|
|
23 ## with df degrees of freedom. |
|
|
24 ## |
|
|
25 ## With the optional argument string alt, the alternative of interest |
|
3426
|
26 ## can be selected. |
|
3200
|
27 ## If alt is "!=" or "<>", the null is tested against the two-sided |
|
|
28 ## alternative mean(x) != mean(y). |
|
|
29 ## If alt is ">", the one-sided alternative mean(x) > mean(y) is used, |
|
3426
|
30 ## similarly for "<". |
|
3200
|
31 ## The default is the two-sided case. |
|
|
32 ## |
|
|
33 ## pval is the p-value of the test. |
|
3426
|
34 ## |
|
3200
|
35 ## If no output argument is given, the p-value of the test is displayed. |
|
3426
|
36 |
|
3200
|
37 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
|
|
38 ## Description: Student's two-sample t test |
|
|
39 |
|
|
40 function [pval, t, df] = t_test_2 (x, y, alt) |
|
3426
|
41 |
|
3200
|
42 if ((nargin < 2) || (nargin > 3)) |
|
3426
|
43 usage ("[pval, t, df] = t_test_2 (x, y [, alt])"); |
|
3200
|
44 endif |
|
3426
|
45 |
|
3200
|
46 if (! (is_vector (x) && is_vector (y))) |
|
|
47 error ("t_test_2: both x and y must be vectors"); |
|
|
48 endif |
|
|
49 |
|
|
50 n_x = length (x); |
|
|
51 n_y = length (y); |
|
|
52 df = n_x + n_y - 2; |
|
|
53 mu_x = sum (x) / n_x; |
|
|
54 mu_y = sum (y) / n_y; |
|
|
55 v = sumsq (x - mu_x) + sumsq (y - mu_y); |
|
|
56 t = (mu_x - mu_y) * sqrt ( (n_x * n_y * df) / (v * (n_x + n_y)) ); |
|
|
57 cdf = t_cdf (t, df); |
|
|
58 |
|
|
59 if (nargin == 2) |
|
|
60 alt = "!="; |
|
|
61 endif |
|
|
62 |
|
|
63 if (! isstr (alt)) |
|
|
64 error ("t_test_2: alt must be a string"); |
|
|
65 endif |
|
|
66 if (strcmp (alt, "!=") || strcmp (alt, "<>")) |
|
|
67 pval = 2 * min (cdf, 1 - cdf); |
|
|
68 elseif strcmp (alt, ">") |
|
|
69 pval = 1 - cdf; |
|
|
70 elseif strcmp (alt, "<") |
|
|
71 pval = cdf; |
|
|
72 else |
|
|
73 error (sprintf ("t_test_2: option %s not recognized", alt)); |
|
|
74 endif |
|
|
75 |
|
|
76 if (nargout == 0) |
|
|
77 printf (" pval: %g\n", pval); |
|
|
78 endif |
|
|
79 |
|
|
80 endfunction |
