Shaffer ( 1986) suggested a modification of the Holm procedure to provide an
additional boost in power. The critical values used in the Shaffer procedure (HS)
are obtained by dividing aFW by the number of tests yet to be conducted in which
the null hypothesis could be true, given the null hypotheses already rejected in
previous steps. For example, in a three-group ANOVA in which the largest differ
ence in sample means is between Groups 1 and 3, if the null hypothesis of JlXj = ji3
is rejected at the first step, then only one of the remaining two pairwise null
hypotheses ([i{ = x2 and |i2 = |i3) logically can be true. Consequently, in this
three-group example, the Shaffer procedure tests the second largest mean differ
ence using apw = oCj^/1, rather than apw = a^/2, as would be used with the Holm
procedure, or apw = 0CpW/3, as would be used with the Dunn procedure