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'.