APPLIED MULTIVARIATE RESEARCH
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the differences among the large coefficients are assumed to be within the bounds
of sampling variability, and thus important information is not lost by converting
these values to 1s and -1s consistent with their original signs (see Rozeboom,
1979, for further discussion of this topic). Again, this is the same process used
when interpreting factors in factor analysis, when creating sum scores from a
factor analysis or multiple regression analysis, and generating contrast coefficients
in analysis of variance from an examination of means.
In words then, the multivariate composite that discriminates between the
European American, Asian American, and Asian International students is higher
Openness-to-Experience relative to lower Extraversion and Agreeableness. A
sensible label to apply to this novel multivariate composite is ‘‘Reserved-Openness.’’
Individuals who score high on this composite are quietly or reservedly
open to new experiences, whereas individuals who score low on this composite
can be described as gregariously traditional (i.e., extraverted, agreeable, and low
on openness). The composite can thus be interpreted as Reserved-Openness vs.
Gregarious-Traditionalism.
The nature of this multivariate composite can further be understood by examining
the means in Figure 1. As can be seen in the highlighted (i.e., the ‘‘boxed’’)
portions of the graph European Americans rate themselves higher on Extraversion
and Agreeableness relative to Openness-to-Experience, whereas Asian Americans
and Asian Internationals rate themselves higher on Openness-to-Experience relative
to Extraversion and Agreeableness. It is thus the pattern of means, or more
specifically the differences in patterns of means, that is captured by the simplified,
multivariate composite. When reporting the results of the analyses for this
particular study, the multivariate effect could possibly be discussed with respect
to cultural differences between Asian and Caucasian Americans in terms of their
personality types. Types, in the realm of personality psychology, are considered
to be multivariate clusters of traits or other stable personal characteristics.
The simplification and interpretation process is perhaps the most important
stage of the MANOVA since it provides the bridge from a purely statistical effect
to a theoretically meaningful effect. If at this point in the analysis the multivariate
composite (i.e., the discriminant function) can not be labeled or theoretically
interpreted, a switch to separate univariate analyses would be prudent. Otherwise,
the researcher will be faced with a situation in which the multivariate effect is
potentially large and statistically significant, but conceptually meaningless.
Because of the importance of interpretation in the current approach toward
MANOVA, a number of pointers for interpreting the multivariate function will be
presented below.
Step 4: Testing the Simplified Multivariate Composite for Statistical Significance.
Do the EA, AA, and AI groups differ significantly in their means on the simplified
composite, Reserved-Openness? Recall the three groups differed significantly
on the full composite, as indicated by the Roy’s g.c.r. test (q = .25, p
< .0005). The mathematics underlying MANOVA will insure the q values are
maximized for each of the linear combinations of dependent variables, subject to
the condition that each is uncorrelated with preceding discriminant functions. The
multivariate composite produced from the simplification process is essentially