Re: ANOVA with selected comparisons?

Hi

On Sat, 22 Nov 2003, Anon. wrote:
> >>Peter Frank wrote:
> >>>I got a question regarding multiple comparison analysis. I have six
> >>>samples and I am only interested in the comparisons of one group of
> >>>three samples to the other group of three samples, which makes 9
> >>>comparisons. Doing an ordinary ANOVA with the SNK post hoc test gives
> >>>me more comparisons than that. Are the results still valid or do I
> >>>have to make any corrections for being only interested in comparing
> >>>one group of samples to the other group of samples and not any sample
> >>>to any other sample?

> Any decent stats software - R, S-PLUS, SAS, and Genstat all do it, and 
> I'll be shocked if SPSS doesn't.
> 
> The model is that each sample has a mean (of the three measurements), 
> and each group has a common mean (of the sample means).  The ANOVA tests 
> whether the group means are the same, and then whether the sample means 
> are the same.  Depending on what package you're using, the way the model 
> is written is different.
> 
> Any decent stats textbook (including those for non-specialists) should 
> describe nested ANOVA, so you should pick your favourite (for example 
> Grafen & Hails' book seems to have got good reviews, it's aimed at 
> biologists but that shouldn't put you off).

Another way to achieve something like this is to do planned
contrasts, rather than pairwise comparisons.  The first contrast
would be: -1 -1 -1 +1 +1 +1 to compare the average of the first 3
groups to the average of the second 3 groups.  This would use 1
of the 6-1 = 5 df for the group effect.  Two of the remaining 4
df could be used to compare the first 3 groups in some meaningful
manner (if possible), and the final 2 df could be used to compare
the second 3 groups.  If the 3 groups within each set were
ordered on some relevant factor, then one could do the polynomial
contrasts within each of the sets (i.e., -1 0 +1, -1 2 -1).  Or
if two of the groups are more similar to one another (e.g., 1 and
2 vs. 3), then special contrasts could be done within each set
(e.g., -1 -1 +2, -1 +1 0).

Although conceptually similar, it may be that the nested and
planned comparison approaches would differ in some manner (e.g.,
different error terms?).

Best wishes
Jim

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James M. Clark                          (204) 786-9757
Department of Psychology                (204) 774-4134 Fax
University of Winnipeg                  4L05D
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CANADA                                  http://www.uwinnipeg.ca/~clark
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