--- /dev/null
+## Copyright (C) 1995-2012 Kurt Hornik
+##
+## 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
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {[@var{pval}, @var{f}, @var{df_b}, @var{df_w}] =} anova (@var{y}, @var{g})
+## Perform a one-way analysis of variance (ANOVA). The goal is to test
+## whether the population means of data taken from @var{k} different
+## groups are all equal.
+##
+## Data may be given in a single vector @var{y} with groups specified by
+## a corresponding vector of group labels @var{g} (e.g., numbers from 1
+## to @var{k}). This is the general form which does not impose any
+## restriction on the number of data in each group or the group labels.
+##
+## If @var{y} is a matrix and @var{g} is omitted, each column of @var{y}
+## is treated as a group. This form is only appropriate for balanced
+## ANOVA in which the numbers of samples from each group are all equal.
+##
+## Under the null of constant means, the statistic @var{f} follows an F
+## distribution with @var{df_b} and @var{df_w} degrees of freedom.
+##
+## The p-value (1 minus the CDF of this distribution at @var{f}) is
+## returned in @var{pval}.
+##
+## If no output argument is given, the standard one-way ANOVA table is
+## printed.
+## @end deftypefn
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Description: One-way analysis of variance (ANOVA)
+
+function [pval, f, df_b, df_w] = anova (y, g)
+
+ if ((nargin < 1) || (nargin > 2))
+ print_usage ();
+ elseif (nargin == 1)
+ if (isvector (y))
+ error ("anova: for `anova (Y)', Y must not be a vector");
+ endif
+ [group_count, k] = size (y);
+ n = group_count * k;
+ group_mean = mean (y);
+ else
+ if (! isvector (y))
+ error ("anova: for `anova (Y, G)', Y must be a vector");
+ endif
+ n = length (y);
+ if (! isvector (g) || (length (g) != n))
+ error ("anova: G must be a vector of the same length as Y");
+ endif
+ s = sort (g);
+ i = find (s (2 : n) > s(1 : (n-1)));
+ k = length (i) + 1;
+ if (k == 1)
+ error ("anova: there should be at least 2 groups");
+ else
+ group_label = s ([1, (reshape (i, 1, k-1) + 1)]);
+ endif
+ for i = 1 : k;
+ v = y (find (g == group_label (i)));
+ group_count (i) = length (v);
+ group_mean (i) = mean (v);
+ endfor
+
+ endif
+
+ total_mean = mean (y(:));
+ SSB = sum (group_count .* (group_mean - total_mean) .^ 2);
+ SST = sumsq (reshape (y, n, 1) - total_mean);
+ SSW = SST - SSB;
+ df_b = k - 1;
+ df_w = n - k;
+ v_b = SSB / df_b;
+ v_w = SSW / df_w;
+ f = v_b / v_w;
+ pval = 1 - fcdf (f, df_b, df_w);
+
+ if (nargout == 0)
+ ## This eventually needs to be done more cleanly ...
+ printf ("\n");
+ printf ("One-way ANOVA Table:\n");
+ printf ("\n");
+ printf ("Source of Variation Sum of Squares df Empirical Var\n");
+ printf ("*********************************************************\n");
+ printf ("Between Groups %15.4f %4d %13.4f\n", SSB, df_b, v_b);
+ printf ("Within Groups %15.4f %4d %13.4f\n", SSW, df_w, v_w);
+ printf ("---------------------------------------------------------\n");
+ printf ("Total %15.4f %4d\n", SST, n - 1);
+ printf ("\n");
+ printf ("Test Statistic f %15.4f\n", f);
+ printf ("p-value %15.4f\n", pval);
+ printf ("\n");
+ endif
+
+endfunction
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff