Mercurial > octave
view scripts/statistics/tests/anova.m @ 21634:96518f623c91
Backed out changeset dcf8922b724b
author | Mike Miller <mtmiller@octave.org> |
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date | Wed, 20 Apr 2016 11:06:03 -0700 |
parents | dcf8922b724b |
children | bac0d6f07a3e |
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## Copyright (C) 1995-2015 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 {} {[@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. ## @seealso{manova} ## @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