🚀 go-pugleaf

I was wondering what the statistical community thinks of the
Sequential Bonferroni test proposed by Holm (1979 Scand
J Statist 6:65-70).  This adjustment attempts to control
Type 1 errors much in the same way that the standard
Bonferroni method, except that it is much more lenient
(powerful).  It works like this:

In an ordinary Bonferroni adjustment, the comparisonwise
error rate (alpha[ind]) is controlled by dividing the
experimentwise error by the number of comparisons to be
made (alpha[exp]/n).  It is known that this tends to 
conservatively set the true experimentwise error <= alpha[exp].

In the sequential Bonferroni method, much the same adjustment
is made, but instead of testing all comparisons at the
alpha[exp]/n level, you only divide alpha[exp] by the number
of tests (or comparisons) remaining.  As soon as you reach
a non-significant result, however, you stop testing.

For example, if the p-values for five different tests were
  0.008 0.01 0.012 0.02 0.04   setting alpha[exp] = 0.05
only the first two tests would be significant by the
standard Bonferroni criteria, but all tests would be
significant by the sequential Bonferroni method.

What do statisticians think of this method?  Predictably, it
has not made it into any text books that I have seen.  It is
becoming popular among population biologists because of a
paper by Rice (1989 Evolution 43:223-225).  Is it OK to use?

Patrick Phillips
University of Texas at Arlington
phil@decster.uta.edu