From bug-octave-request at bevo dot che dot wisc dot edu Tue Feb 10 07:29:30 2004
Subject: anova.m
From: toni saarela <toni dot saarela at helsinki dot fi>
To: bug-octave at bevo dot che dot wisc dot edu
Date: Tue, 10 Feb 2004 15:22:51 +0200

Version: Octave 2.1.50 (i686-pc-linux-gnu)

Description:

I think there's a small bug in anova.m (which performs one-way analysis
of variance). It only occurs when using anova with two input arguments,
as in

octave:1> anova (y,g) 

,where y is a vector containing the data and g is a vector defining the
groups, and only with unequal group sizes.

The total mean is calculated from the group means (see below). This
works fine if the group sizes are equal. However, if they are not, it
gives too much weight to smaller groups in calculation of total mean,
sometimes leading to too high estimates of between-groups variance (and
of total variance), and thus too high F- and too small p-values. 

Example:

octave:1>y = [1 3 4 2 1 5 3 5 6 7 4 5 7 10 11 3]';
octave:2>g = [1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 3]';
octave:3>anova (y, g)

gives F=7.4067, p=0.0071 (ssq between groups = 71.5600)

should be (please correct me if I'm wrong): F=6.3797, p=0.0117 (ssq
between groups = 61.6375)

Fix:
---

Simply replacing the vector group_mean with y (input vector containing
all the data) in calculation of total_mean on line 83 should fix it:

line 83:
   total_mean = mean (group_mean);

to:
   total_mean = mean (y);

Now the SSQ's produce the right result: (lines 84-86)
   SSB = sum (group_count .* (group_mean - total_mean) .^ 2);
   SST = sumsq (reshape (y, n, 1) - total_mean);
   SSW = SST - SSB;

(Or if group_mean is to be used, it should be weighted with relative
group sizes)

Best regards,
Toni Saarela




-------------------------------------------------------------
Octave is freely available under the terms of the GNU GPL.

Octave's home on the web:  http://www.octave.org
How to fund new projects:  http://www.octave.org/funding.html
Subscription information:  http://www.octave.org/archive.html
-------------------------------------------------------------