X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?a=blobdiff_plain;ds=sidebyside;f=octave_packages%2Fm%2Fstatistics%2Ftests%2Fanova.m;fp=octave_packages%2Fm%2Fstatistics%2Ftests%2Fanova.m;h=d2776f09eaedad4d54cd99fbd0e02282bec5ebf4;hb=1c0469ada9531828709108a4882a751d2816994a;hp=0000000000000000000000000000000000000000;hpb=63de9f36673d49121015e3695f2c336ea92bc278;p=CreaPhase.git diff --git a/octave_packages/m/statistics/tests/anova.m b/octave_packages/m/statistics/tests/anova.m new file mode 100644 index 0000000..d2776f0 --- /dev/null +++ b/octave_packages/m/statistics/tests/anova.m @@ -0,0 +1,110 @@ +## 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 +## . + +## -*- 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 +## 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