🚀 go-pugleaf

   The editor of a prestigious journal has written to tell me that he
likes my paper but questions my statistical analysis.  I believe the
editor's point is valid but (1) suspect the problem is of minor
consequence, (2) cannot think of a cure that is worse than the disease,
and (3) see this sort of analysis used all the time.  I would appreciate
comments and advice on the issue.
   The experiment used a 2 X 2 X 2 X 2 between-subjects factorial
design.  Subjects in each condition answered 32 questionnaire items
having a 1-9 scale.  Data analysis was conducted by first reducing
the dimensionality of the data and then using MANOVA.  Principal
component analysis with varimax rotation was used reduce the 32 items
to three orthogonal components that accounted for 67% of the total
variance and were readily interpretable.  Subjects' scores on each of
the three PCs were computed using regression, and these scores were
then entered as DVs in a 4-way MANOVA.  The resulting main effects
and interactions were, if I may say so, beautiful, enlightening,
and, best of all, predicted.
   Now for my problem.  The editor objects that the PCA confounds
within-cell and between-cell covariation, thus causing the results of
the PCA and the MANOVA to be partly overlapping to some unknown extent.
That is, the results of the PCA stem both from the covariation among
items independent of the experimental manipulations and from the
covariation among items resulting from the experimental treatments.
   Is this really a problem?  I've never encountered the objection
before.  I don't want to abandon the PCA, because the pattern of
loadings itself has theoretical significance for the arguments I wish to
make.  One can imagine trying to partial out average within-cell
covariation before doing the PCA, but this would seem to introduce
problems of its own.  I am an experimental psychologist, not a
statistician, and I would greatly appreciate input from members of this
list.  I will summarize for the list comments sent to me.

Jerry Parrott
Dept of Psychology
Georgetown University
Washington, DC  20057
GU86@GUVM.BITNET