Re: anova.m

Sorry for dropping this until now.

I made the change you suggested.

Thanks,

jwe


On 10-Feb-2004, Andy Adler wrote:

| 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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