Imagine you have a large number of measures. For example,
you have given your new questionnaire, which has 40
questions, to 100 people. You have 4000 scores. This is far
too much for you to easily make sense of. Factor analysis
allows you to reduce this mass of data to a smaller, more
manageable amount.
It works a little bit like regression to find
factors. Factors are new measures that summarise
your data. Imagine your questionnaire asks one particular
question five times in different ways. You'd expect people
to give much he same answer each time. In other words, the
scores from the five questions would be highly
inter-correlated. If somebody responds in a particular way
to one of the questions, we know that they will respond the
same way to the others. Therefore, rather than present the
same information five times, it'd be better to summarise
it. You would do this with a factor. For example, if the
questions were 'do you like cats?', 'are cats nice?', 'do
you hate cats?' and so on, you could reduce the five scores
that each person gives to one factor, which we might call
'cat attitude'.
Once you have identified your factors, you can describe the
extent to which each question belongs to that factor. This
is expressed with a loading. A factor loading is simply a
correlation coefficient, which tells us the extent to which
a question is measuring that factor. So in the above
example, we would expect 'do you like cats?' to have a high
positive loading on the 'cat attitude' factor. We would
expect 'do you hate cats?' to have a high negative loading.
A question such as 'do you like beer?' should have a
loading of close to zero, as this is irrelevant to cat
attitudes. Similarly, the questions about whether you like
cats would have a loading of close to zero if we were
considering a different factor, such as 'drink
preferences'.
When you do an analysis, you have to decide how many
factors your data contain. There are two criteria -
Eigenvalue One (aka Kaiser's criterion) or the Scree Plot.
In the end your choice of how many factors to extract from
your data will involve judgement, as will naming your
factors.
It is done with Analyse > data reduction >
factor...
Don't forget to request a scree plot and to set the
rotation to 'varimax'. If you want to produce factor scores
select the 'save as variables' option and leave the method
on 'regression'.