|
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 |
|
3454
|
17 ## -*- texinfo -*- |
|
|
18 ## @deftypefn {Function File} {[@var{pval}, @var{z}] =} z_test (@var{x}, @var{m}, @var{v}, @var{alt}) |
|
|
19 ## Perform a Z-test of the null hypothesis @code{mean (@var{x}) == |
|
|
20 ## @var{m}} for a sample @var{x} from a normal distribution with unknown |
|
|
21 ## mean and known variance @var{v}. Under the null, the test statistic |
|
|
22 ## @var{z} follows a standard normal distribution. |
|
3200
|
23 ## |
|
3454
|
24 ## With the optional argument string @var{alt}, the alternative of |
|
|
25 ## interest can be selected. If @var{alt} is @code{"!="} or |
|
|
26 ## @code{"<>"}, the null is tested against the two-sided alternative |
|
|
27 ## @code{mean (@var{x}) != @var{m}}. If @var{alt} is @code{">"}, the |
|
|
28 ## one-sided alternative @code{mean (@var{x}) > @var{m}} is considered, |
|
|
29 ## similarly for @code{"<"}. The default is the two-sided case. |
|
3200
|
30 ## |
|
3454
|
31 ## The p-value of the test is returned in @var{pval}. |
|
3426
|
32 ## |
|
3200
|
33 ## If no output argument is given, the p-value of the test is displayed |
|
3426
|
34 ## along with some information. |
|
3454
|
35 ## @end deftypefn |
|
3200
|
36 |
|
|
37 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
|
|
38 ## Description: Test for mean of a normal sample with known variance |
|
|
39 |
|
|
40 function [pval, z] = z_test (x, m, v, alt) |
|
3426
|
41 |
|
3200
|
42 if ((nargin < 3) || (nargin > 4)) |
|
|
43 usage ("[pval, z] = z_test (x, m, v [, alt])"); |
|
|
44 endif |
|
3426
|
45 |
|
3200
|
46 if (! is_vector (x)) |
|
|
47 error ("z_test: x must be a vector."); |
|
|
48 endif |
|
|
49 if (! is_scalar (m)) |
|
|
50 error ("z_test: m must be a scalar."); |
|
|
51 endif |
|
|
52 if (! (is_scalar (v) && (v > 0))) |
|
|
53 error ("z_test: v must be a positive scalar."); |
|
|
54 endif |
|
3426
|
55 |
|
3200
|
56 n = length (x); |
|
|
57 z = sqrt (n/v) * (sum (x) / n - m); |
|
|
58 cdf = stdnormal_cdf (z); |
|
3426
|
59 |
|
3200
|
60 if (nargin == 3) |
|
|
61 alt = "!="; |
|
|
62 endif |
|
|
63 |
|
|
64 if (! isstr (alt)) |
|
|
65 error ("z_test: alt must be a string"); |
|
|
66 elseif (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 ("z_test: option %s not recognized", alt)); |
|
|
74 endif |
|
3426
|
75 |
|
3200
|
76 if (nargout == 0) |
|
|
77 s = strcat ("Z-test of mean(x) == %g against mean(x) %s %g,\n", |
|
3426
|
78 "with known var(x) == %g:\n", |
|
|
79 " pval = %g\n"); |
|
3200
|
80 printf (s, m, alt, m, v, pval); |
|
|
81 endif |
|
|
82 |
|
|
83 endfunction |
