Mercurial > octave-antonio
annotate scripts/statistics/tests/anova.m @ 11472:1740012184f9
Use uppercase for variable names in error() strings to match Info documentation. Only m-files done.
| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Sun, 09 Jan 2011 21:33:04 -0800 |
| parents | 16f53d29049f |
| children | fd0a3ac60b0e |
| rev | line source |
|---|---|
| 7017 | 1 ## Copyright (C) 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2005, 2006, |
| 9245 | 2 ## 2007, 2009 Kurt Hornik |
| 3426 | 3 ## |
| 3922 | 4 ## This file is part of Octave. |
| 5 ## | |
| 6 ## Octave is free software; you can redistribute it and/or modify it | |
| 7 ## under the terms of the GNU General Public License as published by | |
| 7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
| 9 ## your option) any later version. | |
| 3426 | 10 ## |
| 3922 | 11 ## Octave is distributed in the hope that it will be useful, but |
| 3200 | 12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
| 13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 3426 | 14 ## General Public License for more details. |
| 15 ## | |
| 3200 | 16 ## You should have received a copy of the GNU General Public License |
| 7016 | 17 ## along with Octave; see the file COPYING. If not, see |
| 18 ## <http://www.gnu.org/licenses/>. | |
| 3200 | 19 |
| 3454 | 20 ## -*- texinfo -*- |
| 21 ## @deftypefn {Function File} {[@var{pval}, @var{f}, @var{df_b}, @var{df_w}] =} anova (@var{y}, @var{g}) | |
| 22 ## Perform a one-way analysis of variance (ANOVA). The goal is to test | |
| 23 ## whether the population means of data taken from @var{k} different | |
| 24 ## groups are all equal. | |
| 3200 | 25 ## |
| 3454 | 26 ## Data may be given in a single vector @var{y} with groups specified by |
| 27 ## a corresponding vector of group labels @var{g} (e.g., numbers from 1 | |
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28 ## to @var{k}). This is the general form which does not impose any |
| 3454 | 29 ## restriction on the number of data in each group or the group labels. |
| 3200 | 30 ## |
| 3454 | 31 ## If @var{y} is a matrix and @var{g} is omitted, each column of @var{y} |
| 32 ## is treated as a group. This form is only appropriate for balanced | |
| 33 ## ANOVA in which the numbers of samples from each group are all equal. | |
| 3200 | 34 ## |
| 3454 | 35 ## Under the null of constant means, the statistic @var{f} follows an F |
| 36 ## distribution with @var{df_b} and @var{df_w} degrees of freedom. | |
| 37 ## | |
| 38 ## The p-value (1 minus the CDF of this distribution at @var{f}) is | |
| 39 ## returned in @var{pval}. | |
| 3200 | 40 ## |
| 41 ## If no output argument is given, the standard one-way ANOVA table is | |
| 42 ## printed. | |
| 3454 | 43 ## @end deftypefn |
| 3200 | 44 |
| 5428 | 45 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
| 3456 | 46 ## Description: One-way analysis of variance (ANOVA) |
| 3426 | 47 |
| 3200 | 48 function [pval, f, df_b, df_w] = anova (y, g) |
| 3426 | 49 |
| 3200 | 50 if ((nargin < 1) || (nargin > 2)) |
| 6046 | 51 print_usage (); |
| 3200 | 52 elseif (nargin == 1) |
| 4030 | 53 if (isvector (y)) |
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Use uppercase for variable names in error() strings to match Info documentation. Only m-files done.
Rik <octave@nomad.inbox5.com>
parents:
9245
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54 error ("anova: for `anova (Y)', Y must not be a vector"); |
| 3200 | 55 endif |
| 56 [group_count, k] = size (y); | |
| 57 n = group_count * k; | |
| 58 group_mean = mean (y); | |
| 59 else | |
| 4030 | 60 if (! isvector (y)) |
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11472
1740012184f9
Use uppercase for variable names in error() strings to match Info documentation. Only m-files done.
Rik <octave@nomad.inbox5.com>
parents:
9245
diff
changeset
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61 error ("anova: for `anova (Y, G)', Y must be a vector"); |
| 3200 | 62 endif |
| 63 n = length (y); | |
| 4030 | 64 if (! isvector (g) || (length (g) != n)) |
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11472
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Use uppercase for variable names in error() strings to match Info documentation. Only m-files done.
Rik <octave@nomad.inbox5.com>
parents:
9245
diff
changeset
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65 error ("anova: G must be a vector of the same length as Y"); |
| 3200 | 66 endif |
| 67 s = sort (g); | |
| 68 i = find (s (2 : n) > s(1 : (n-1))); | |
| 69 k = length (i) + 1; | |
| 70 if (k == 1) | |
| 3456 | 71 error ("anova: there should be at least 2 groups"); |
| 3200 | 72 else |
| 3273 | 73 group_label = s ([1, (reshape (i, 1, k-1) + 1)]); |
| 3200 | 74 endif |
| 75 for i = 1 : k; | |
| 76 v = y (find (g == group_label (i))); | |
| 77 group_count (i) = length (v); | |
| 78 group_mean (i) = mean (v); | |
| 79 endfor | |
| 3426 | 80 |
| 3200 | 81 endif |
| 3426 | 82 |
| 5373 | 83 total_mean = mean (y(:)); |
| 3200 | 84 SSB = sum (group_count .* (group_mean - total_mean) .^ 2); |
| 3426 | 85 SST = sumsq (reshape (y, n, 1) - total_mean); |
| 3200 | 86 SSW = SST - SSB; |
| 87 df_b = k - 1; | |
| 88 df_w = n - k; | |
| 89 v_b = SSB / df_b; | |
| 90 v_w = SSW / df_w; | |
| 91 f = v_b / v_w; | |
| 92 pval = 1 - f_cdf (f, df_b, df_w); | |
| 3426 | 93 |
| 3200 | 94 if (nargout == 0) |
| 95 ## This eventually needs to be done more cleanly ... | |
| 96 printf ("\n"); | |
| 97 printf ("One-way ANOVA Table:\n"); | |
| 98 printf ("\n"); | |
| 99 printf ("Source of Variation Sum of Squares df Empirical Var\n"); | |
| 100 printf ("*********************************************************\n"); | |
| 101 printf ("Between Groups %15.4f %4d %13.4f\n", SSB, df_b, v_b); | |
| 102 printf ("Within Groups %15.4f %4d %13.4f\n", SSW, df_w, v_w); | |
| 103 printf ("---------------------------------------------------------\n"); | |
| 104 printf ("Total %15.4f %4d\n", SST, n - 1); | |
| 105 printf ("\n"); | |
| 3426 | 106 printf ("Test Statistic f %15.4f\n", f); |
| 3200 | 107 printf ("p-value %15.4f\n", pval); |
| 108 printf ("\n"); | |
| 3426 | 109 endif |
| 110 | |
| 3200 | 111 endfunction |