## Copyright (C) 1995, 1996, 1997 Kurt Hornik ## ## This program 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 2, or (at your option) ## any later version. ## ## This program 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 this file. If not, write to the Free Software Foundation, ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. ## Performs a one-way analysis of variance (ANOVA). The goal is to test ## whether the population means of data taken from k different groups ## are all equal. ## ## anova (y, g) provides all data in a single vector y; g is the vector ## of corresponding group labels (e.g., numbers from 1 to k). This is ## the general form which does not impose any restriction on the number ## of data in each group or the group labels (other than that they must ## be scalars). ## ## anova (y), where y is a matrix, treats each column as a group. This ## form is only appropriate for balanced ANOVA where the numbers of ## samples from each group are all equal. ## ## Under the null of constant means, the statistic f follows an F ## distribution with df_b and df_w degrees of freedom. pval is the ## p-value (1 minus the CDF of this distribution at f) of the test. ## ## If no output argument is given, the standard one-way ANOVA table is ## printed. ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> ## Description: One-way analysis of variance (ANOVA) function [pval, f, df_b, df_w] = anova (y, g) if ((nargin < 1) || (nargin > 2)) usage ("anova (y [, g])"); elseif (nargin == 1) if (is_vector (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 (! is_vector (y)) error ("anova: for `anova (y, g)', y must be a vector"); endif n = length (y); if (! is_vector (g) || (length (g) != n)) error (["anova: for `anova (y, g)', g must be a vector", ... " of the same length 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 (group_mean); 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 - f_cdf (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

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