Re: [R] Anova with Scheffe Tests

From: Rogers, James A [PGRD Groton] <>
Date: Thu 03 Mar 2005 - 00:35:14 EST

>In good ol' Statview (now dearly departed) to complete a Scheffe
>test you selected the independent variables and dependent variable
>and it produced a table with the pairwise comparisons of the levels
>of the factor. I'm looking for a system that is as basic, but can be
>done using R and has documentation so I'm not guessing what I'm
>doing. I'd rather not have to do plots in R and then run over to
>dead software to do Scheffe's if possible.
>I checked on google and there seems to be code for a couple of
>functions out there, but I need something that has a manual.
>Is there a Scheffe function out there that is reasonably well
>documented, or should I consider some other method of dealing with
>this data. We have been using Scheffe for this type of analysis as I
>was under the impression it was very conservative. Tukey's HSD seems
>to be conservative as well. Should I try this? Is there a different
>approacch that is better and where can I read about it.
>Thanks for any help you can provide.

It sounds like you are only interested in simple pairwise comparisons, in which case you are better off using Tukey's HSD. This will still protect the family-wise error rate, but will allow you to infer more differences than you would using Scheffé's method. Scheffé's method is exact if you are truly interested in all contrasts (a situation I have never come across), but it is overly conservative when inferences are only made for pairwise differences.

A geometric explanation of the difference between the two methods can be found in Jason Hsu's book "Multiple Comparisons: Theory and Methods".

As you can also read in that book, there is no good reason to precede Tukey's HSD with an ANOVA F-test. Tukey's HSD controls the family-wise error rate anyway, so an initial F-test is superfluous.


James A. Rogers
Manager, Nonclinical Statistics
PGR&D Groton Labs
Eastern Point Road (MS 8260-1331)
Groton, CT 06340
office: (860) 686-0786
fax: (860) 715-5445  

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