[R] explaining curious result of aov

[Prof Brian Ripley]

The ANOVA assumes equal variances in the groups.  Suppose groups 5 and 6 
had much lower variances than groups 1 to 4, and group 6 had a different 
mean from the other 5 (which were about equal)?

Given how small the groups apperat to be, this could happen.

On Tue, 21 Oct 2003, Bill Shipley wrote:

> Hello.  I have come across a curious result that I cannot explain.
> Hopefully, someone can explain this.  I am doing a 1-way ANOVA with 6
> groups (example: summary(aov(y~A)) with A having 6 levels).  I get an F
> of 0.899 with 5 and 15 df (p=0.51).  I then do the same analysis but
> using data only corresponding to groups 5 and 6.  This is, of course,
> equivalent to a t-test.  I now get an F of 142.3 with 1 and 3 degrees of
> freedom and a null probability of 0.001.  I know that multiple
> comparisons changes the model-wise error rate, but even if I did all 15
> comparisons of the 6 groups, the Bonferroni correction to a 5% alpha is
> 0.003, yet the Bonferroni correction gives conservative rejection
> levels.
> 
> How can such a result occur?  Any clues would be helpful.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595