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pairs of means are evaluated at the same value of
q.
The
expression “single step” indicates that the test does not
take into account by how many steps the means in the
pairwise comparison are separated.
Two tests available in SPSS and SAS were not included in Table 7.1
because they did not fit the format we used for the table. The
Wa l l e r-
Duncan
test in SPSS is based on Bayesian statistical principles, an approach
that focuses on various types of probability distributions. If you use it,
you must specify a
TypeIError/TypeIIErrorratio
. As a guide, ratios of
50, 100, and 500 generally match up with alpha levels of .10, .05, and .01.
If you do not have equal sample sizes, the result is an approximation. The
Dunnett test is conceptually similar to one of the preset contrasts, and we
will include it in our discussion of this next group of multiple comparison
procedures (see Section 7.15.2.6).
7.8.3.2 Homogeneity of Variance Not Assumed
There are four multiple comparison procedures available in SPSS that can
be applied when you cannot assume that the groups have comparable
variances. The
Games-Howell
,
Dunnett T3
, and
Dunnett C
tests are all
based on variations of the Studentized range distribution; the
Tamhane
T2
is based on the
t
distribution.
7.8.4 SOME GUIDELINES IN SELECTING TESTS
To say that there is a good deal of agreement on which tests to use for
a posteriori comparisons would be to adopt a very optimistic attitude in
viewing the literature. The major point of agreement is this: If you cannot
assume homogeneity of variance, then use one of the tests that do not
assume it. After that, the decision process gets complicated.
After they have settled the homogeneity of variance issue, the primary
decision basis that many researchers use in deciding which of these tests
to apply is power. Their choice would be at least in part determined by the
temperament of the researchers - that is, by the level of risk with which
the researchers felt comfortable in the particular research context. We will
offer our mild suggestions because we do not want to leave you entirely
without input but, because most readers are likely to be students, we urge
you to talk with your professors about their thoughts on this matter.
We consider first the small group of four tests where homogeneity of
variance cannot be assumed. Generally, the Games-Howell test is more
powerful than the Dunnett C. With large error degrees of freedom, Dun-
nett's C is more powerful than his T3, but with small error degrees of
freedom that relationship is reversed (Kirk, 1995). The Tamhane T2 test is
probably the most conservative of the group. We would give a mild nod to
Games-Howell if the situation calls for a bit of power; if your preferences
lie toward the other end of the continuum, then we would mildly suggest
the more conservative Tamhane T2.
