Stat question: Bonferoni for a priori analyses?

Rick Boyce Richard.L.Boyce at dartmouth.edu
Tue Nov 16 10:04:02 EST 1993


In article <1993Nov15.164929.2378 at mnemosyne.cs.du.edu>
anon1167 at nyx.cs.du.edu (M) writes:

> I am doing some analyese where I am comparing a small number of 
> treatment groups to a control group, using _t_ tests.  For complicated
> reasons I can't use a multiple comparision procuedure such as Dunnet's
> test.  My question is, since I am testing, in an a priori fashion, only a
> subset of all of the possible comparisons, do I really need to to a
> Bonferoni correction?  I seem to recall from grad school someone telling
> me that bonferoni is only necessary when you're making post-hoc
> comparisons; if you're making a priori comparisions, it is not necessary.
> 
> I can't, however, find any references re: this.  

An excellent article on these matters is:  Day, R.W. & Quinn, G.P. 
1989.  Comparisons of treatments after an analysis of variance in
ecology.  Ecology 59:433-463.  

Before I'd recommend a procedure I would want to know if your variances
are equal, as many of the tests are valid only if this is so (is this
why you can't use Dunnett's test?).  Since you are comparing several
treatments to a control and I presume that you want to know which
particular treatments are different from the control, you can't use
single-df orthogonal contrasts.  As long as you stick to your planned
comparisons, you can use the LSD (least significant difference).  If
you have heterogeneous variances, Day & Quinn recommend the Welch t
test.  For non-parametric planned comparisons, you can use the
Fligner-Policello test; there is a modification of this test with
significance levels adjusted by the Dunn-Sidak method that is the
equivalent of Dunnett's test.  If you want to do other comparisons
suggested by the data, then there are an array of other tests,
including Bonferroni, which are appropriate.  Day & Quinn gives the
formulas needed for each test, the assumptions and suitability of each
test, and their recommendations.  I hope this helps.
======================================================================
Rick Boyce
Richard.L.Boyce at dartmouth.edu



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