User Guide

387
GLM Univariate
Analysis
multiple comparison tests are performed for the average across the levels of the
within-subjects factors. For GLM Multivariate, the post hoc tests are performed for
each depend
ent variable separately. GLM Multivariate and GLM Repeated Measures
are available only if you have the Advanced Models option installed.
The Bonferroni and Tukey’s honestly significant difference tests are commonly
used multip
le comparison tests. The Bonferroni test, based on Student’s t statistic,
adjusts the observed significance level for the fact that multiple comparisons are
made. Sidak’s t test also adjusts the significance level and provides tighter bounds
than the Bo
nferroni test. Tukey’s honestly significant difference test uses the
Studentized range statistic to make all pairwise comparisons between groups and sets
the experimentwise error rate to the error rate for the collection for all pairwise
comparis
ons. When testing a large number of pairs of means, Tukey’s honestly
significant difference test is more powerful than the Bonferroni test. For a small
number of pairs, Bonferroni is more powerful.
Hochberg
’s GT2 is similar to Tukey’s honestly significant difference test, but
the Studentized maximum modulus is used. Usually, Tukey’s test is more powerful.
Gabriel’s pairwise comparisons test also uses the Studentized maximum modulus
and is ge
nerally more powerful than Hochberg’s GT2 when the cell sizes are unequal.
Gabriel’s test may become liberal when the cell sizes vary greatly.
Dunnett’s pairwise multiple comparison t test compares a set of treatments
against
a single control mean. The last category is the default control category.
Alternatively, you can choose the first category. You can also choose a two-sided or
one-sided test. To test that the mean at any level (except the control category) of the
factor
is not equal to that of the control category, use a two-sided test. To test whether
the mean at any level of the factor is smaller than that of the control category, select
<
Control
. Likewise, to test whether the mean at any level of the factor is larger than that
of the
control category, select
>Control.
Ryan, Einot, Gabriel, and Welsch (R-E-G-W) developed two multiple step-down
range tests. Multiple step-down procedures first test whether all means are equal.
If all
means are not equal, subsets of means are tested for equality. R-E-G-W F is
based on an F test and R-E-G-W Q is based on the Studentized range. These tests
are more powerful than Duncan’s multiple range test and Student-Newman-Keuls
(whi
ch are also multiple step-down procedures), but they are not recommended
for unequal cell sizes.
When the variances are unequal, use Tamhane’s T2 (conservative pairwise
comp
arisons test based on a t test), Dunnett’s T3 (pairwise comparison test based
on the Studentized maximum modulus), Games-Howell pairwise comparison