Still we should recognize that the factors measured by the test may act as a surrogate for the ability to do the job. And that the surrogate shares a certain amount of common variance with the criterion measure under the particular circumstances in which we have observed the relationship. We know that many variables affect the substance and reliability candidates' test responses. We consider the effect of aptitudes, knowledge, convictions, discernment of the context, experience with the content, modes of expression, and so on. We look at correlations among measures to see persistent ways of acting, knowing that errors of measurement and sample selection affect the correlations.
Factor analysis provides a way to summarize the information latent in correlations.
We decide what issues are common to a group of tests. The next factor has as much as possible in common with all the remaining variance. Analysts use both geometry and mathematics. Then they find a new vector, which is the least-squares best fit to all the other vectors. The next factor is the best fit to the residuals.