One-Way Between-Subjects Design - Analysis of Variance Designs - page 90

6.4 OMNIBUS AND SIMPLIFYING ANALYSES
6.4.1 THE OMNIBUS ANALYSIS
The summary table for our numerical example shows the results of what
is called the omnibus analysis . An omnibus analysis is the overall ANOVA
that we have been talking about thus far in the topic. It evaluates the effect
of one or more independent variables.
6.4.2 SIMPLIFYING ANALYSES
In the rare instance in which the experimental design has only one in-
dependent variable with exactly two levels, a statistically significant F
ratio informs us that the means of the two conditions are reliably dif-
ferent. The reason for this is because there are only two groups in
the analysis; thus, there is only one pair of means that are being com-
pared and the statistically significant F ratio pertains to that single paired
comparison.
With three or more groups in the analysis, the situation is ordinarily
ambiguous. Yes, with a statistically significant F ratio we can assume that
there is a pair of means that differ; the question is which pair since there
are several alternatives. In a three-group study, for example, the first and
second groups may differ, the first and third groups may differ, and/or
the second and third groups may differ. Under these circumstances, it is
necessary to engage in further analyses to determine between which means
the statistically significant mean differences lie. Such a process examines
pairs of means to determine if they are significantly different. Think of
the omnibus analysis as reflecting a “global,” “macroscopic,” “general,”
or “overall” analysis; then the post-ANOVA-looking-at-pairs-of-means
procedure can be conceived as a “finer-grained, “microscopic,” or “sim-
plifying” level of analysis. It is simplifying in the sense that we analyze
separate portions of the data set rather than analyzing the data set as a
whole.
In the present example, we have five groups. We have obtained a
statistically significant F ratio, but we do not automatically know which
means are significantly different from each other. It is therefore necessary
to perform an additional simplifying procedure on the data to examine
pairs of means. This simplifying procedure in the case of an effect of a
single independent variable, such as we have here, is known, in general,
as a multiple comparisons procedure . However, there are enough different
approaches to performing such multiple comparisons that we will devote
the entirety of Chapter 7 to this topic, using our numerical example of
SAT study time.
6.4.3 EFFECT OF INTEREST IN THIS DESIGN
With only one independent variable in the design, there is only one F ratio
in the omnibus analysis that interests us - the F ratio associated with the