Russel-Research-Method-in-Anthropology

Multivariate Analysis 677
Factor Analysis and Scales
As I mentioned in chapter 12, factor analysis is widely used across the
social sciences in building reliable, compact scales for measuring social and
psychological variables. Suppose, for example, you are interested in attitudes
toward gender role changes among women. You suspect that the underlying
forces of role changes are related to premarital sexuality, working outside the
home, and the development of an independent social and economic life among
women. You make up 50 attitudinal items and collect data on those items from
a sample of respondents.
Factor analysis will help you decide whether the 50 items you made up
really test for the underlying forces you think are at work. If they do, then you
could use a few benchmark items—the ones that ‘‘load high’’ on the factors—
and this would save you from having to ask every respondent about all 50
items you made up. You would still get the information you need—or much
of it, anyway. How much? The amount would depend on how much variance
in the correlation matrix each of your factors accounted for.
The notion of variance is very important here. Factors account for chunks
of variance—the amount of dispersion or correlation in a correlation matrix.
Factors are extracted from a correlation matrix in the order of the amount of
variance that they explain in the matrix. Some factors explain a lot of variance,
while others may be very weak and are discarded by researchers as not being
useful. In a dense matrix, only one or a few factors may be needed to account
for a lot of variance, while in a dispersed matrix, many factors may be needed.
The most common statistical solution for identifying the underlying factors
in a correlation matrix is called the orthogonal solution. In orthogonal factor
analyses, factors are found that have as little correlation with each other as
possible. Other solutions that result in intercorrelated factors are also possible
(the various solutions are options that you can select in all the major statistical
packages, like SAS, SYSTAT, and SPSS). Some researchers say that these
solutions, although messier than orthogonal solutions, are more like real life.
So-called factor loadings are the correlations between the factors and the
variables that are subsumed by, or appear to be components of, factors. All
the old variables ‘‘load’’ on each new factor. The idea is to establish some
cutoff below which you would not feel comfortable accepting that an old variable
loaded onto a factor. Many researchers use 0.50 as the cutoff, and look
at loadings of 0.30–.49 as worth considering. Some researchers insist that a
variable should load at least 0.60 before accepting it as an unambiguous component
of a factor and look at variables that load between 0.30 and 0.59 as
worth considering.
Once you have a list of variables that load high on a factor (irrespective of