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anova.m
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1997-02-26
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4KB
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106 lines
## 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