From bug-octave-request at bevo dot che dot wisc dot edu Tue Feb 10 13:37:10 2004
Subject: Re: anova.m
From: Andy Adler <adler at site dot uottawa dot ca>
To: toni saarela <toni dot saarela at helsinki dot fi>
cc: bug-octave at bevo dot che dot wisc dot edu
Date: Tue, 10 Feb 2004 14:36:45 -0500 (EST)

The anovan.m code in octave-forge has the correct result in
this case.

> y = [1 3 4 2 1 5 3 5 6 7 4 5 7 10 11 3]';
> g = [1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 3]';
> anovan(y, g)
    1-way ANOVA Table (Factors A,):

    Source of Variation        Sum Sqr   df      MeanSS    Fval   p-value
    *********************************************************************
    Error                       62.80    13       4.83
    Factor               A      61.64     2      30.82    6.380  0.011737

> anova(y, g)

    One-way ANOVA Table:

    Source of Variation   Sum of Squares    df  Empirical Var
    *********************************************************
    Between Groups               71.5600     2        35.7800
    Within Groups                62.8000    13         4.8308
    ---------------------------------------------------------
    Total                       134.3600    15

    Test Statistic f              7.4067
    p-value                       0.0071


(Aside: I'm still looking for testers of my anonan code. It's quite
 complex, and I suspect there are still bugs)


Andy


On Tue, 10 Feb 2004, toni saarela wrote:

> 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
>
>
>
>
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