Multiple Comparison Procedures - Analysis of Variance Designs - page 119

that were not planned or specified prior to the omnibus ANOVA but are
computed only after a statistically significant F ratio has been obtained.
Most of the post hoc tests involve performing all possible pairwise com-
parisons. This approach is atheoretical, exploratory, and most certainly
a posteriori. SPSS has a Post Hoc dialog window available in almost all
of its ANOVA procedures, and SAS has drop-down menus in its ANOVA
procedures that contain its post hoc tests. SPSS has eighteen post hoc tests
available and SAS has ten. Alpha inflation becomes of great concern here,
especially if many comparisons are made. We discuss post hoc tests in
Section 7.8.
7.7.2 PRESET CONTRASTS
A second approach to multiple comparisons is the strategy of using what
we are calling preset contrasts. SPSS has a Contrasts dialog window avail-
able in its General Linear Model procedures; about half a dozen different
already structured contrasts are available through that window; SAS has
just a couple on its drop-down menu. The approach of using preset con-
trasts is more restrained than the post hoc test approach in that fewer
than the maximum number of comparisons is performed. Some of the
comparisons that are available are pairwise and others are composite;
furthermore, some are orthogonal and others are nonorthogonal. These
contrasts may be used in an atheoretical or exploratory mode, but they
may also be used to make comparisons that were planned on the basis of
some model prior to the data collection. We discuss preset contrasts in
Section 7.15.
7.7.3 POLYNOMIAL CONTRASTS
One type of preset contrast has a sufficiently different emphasis to warrant
separate treatment here. It is known as polynomial contrasts , and the type
of analysis that one performs using these contrasts is commonly called a
trend analysis . A trend analysis is used to explicate the shape of the function
depicting the means of the groups. In plotting this function, groups are
represented on the x axis and the dependent variable is represented on
the y axis. The means of the groups are then placed in this grid and are
then connected to reveal the shape of the function. We discuss polynomial
contrasts in Section 7.21.
7.7.4 USER-DEFINED CONTRASTS
A fourth approach to multiple comparisons is to engage in user-defined
contrasts. This is the most theoretical and often the most rational approach
to the issue of post-ANOVA comparisons of means. The researchers specify
which groups or combinations of groups will be compared to which others
in advance of data collection, and then proceed to carry out that plan
usually but not necessarily after the ANOVA. Under this strategy, relatively
few comparisons are typically made, and they may be either orthogonal
or nonorthogonal. We discuss user-defined contrasts in Section 7.26.