If we are reasonably confident that the questions in a multi-item set are consistent,
we generally use some method to aggregate all the answers in the set into one aggregate
answer for that set. There are two major options for aggregating.
First is simple summation
or averaging into a single score. For example, if there are five questions relating to satisfaction, we might sum
or average the answers to come to an aggregated satisfaction score. Chapter 6 demonstrated
how to do this.
Second is factor analysis and similar methods. Factor analysis can assess the items from multiple multi-item scales and explore
whether they separate out into their different variables. For instance, say you have
multiple survey items for each of four different variables (satisfaction, trust, service
quality and support). We want two things for such scales:
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Convergent validity: This is similar to internal reliability, in that it assesses whether groups of variables
get consistent and similar patterns of responses. Does it look like they seem to stick
together and indicate a single underlying variable? (Therefore, are the responses
to the satisfaction items convergent in that they are consistent?)
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Discriminant validity: Although we’re happy that the satisfaction items load together, we don’t want any
satisfaction items to stick with any items from other variables like trust. What we
really want is for each set of separate variable items to stick together in their
own cluster, separate from the clusters of other variables. This is called discriminant validity.
There are two different types of factor analysis that can help assess, for multiple
items from multiple variables, whether the items separate out into discernible sets
of variable items (e.g. all the satisfaction items together, all the trust items together,
and little overlap):
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Exploratory factor analysis (principal component analysis and common factor analysis) goes ”looking for" underlying
constructs. You present the statistics program with a list of variables and it sorts
these into groups (factors) based on overlaps of correlation. This approach is most
often used when you have no idea beforehand of what the factor/variable sets of items
are expected to be.
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Confirmatory factor analysis tests whether pre-specified groups of variables do belong in factors, and it forms
the factors for you. In other words, you pre-specify that the following set of variables
should belong to a satisfaction variable, the second set of variables are expected
to belong to a trust factor, and so forth. The program will then tell you the extent
to which your pre-specified pattern agrees with or fits with the actual data responses,
based on variable correlations and overlaps.
Once you have a factor analysis solution that seems to work for your analysis (i.e.
the satisfaction items form one discernible factor, the trust items another, and so
on, perhaps with some acceptable overlap) then SAS can form single variable scores
for each observation on each factor based on this solution. In our example, each survey
respondent can now be given a single score for their satisfaction, a single trust
score, etc. This is a more complex and satisfactory way of aggregating your multi-item
scales into single variable scores.
This book does not discuss factor analysis further; the interested reader should follow
up in more advanced and specialized texts.
Once you have completed the tasks of data checking, cleaning, and preparation into
final variables, you can now proceed to actual data analysis, ranging from basic descriptive
statistics and associations of final constructs (already discussed in Chapters 7 and
8) to more complex techniques such as regression discussed later in the book.