Common Errors in Statistics (and How to Avoid Them), 4th Edition

FACTOR ANALYSIS

The procedures that are involved in factor analysis (FA) as used by psychologists today have several features in common with the procedures for administering Rorschach inkblots. In both procedures, data are first gathered objectively and in quantity; subsequently, the data are analysed according to rational criteria that are time-honoured while not fully understood. … 

—Chris Brand

Alas, the ad-hoc nature of factor analysis is such that one cannot perform the analysis without displeasing somebody. For example, while one group of researchers might argue that a majority of variables should end up identified principally with just one factor, an equally vociferous opposition considers it folly to break up clear g factors by an obsessional search for simple structure.

A factor analysis ought be given the same scrutiny as any other modeling procedure and validated as described in Chapter 15. Godino, Batanero, and Jaimez [2001] note that the following errors are frequently associated with factor analysis:

• Applying it to datasets with too few cases in relation to the number of variables analyzed (less than two cases per variable in a thesis), without noticing that correlation coefficients have very wide confidence intervals in small samples.
• Using oblique rotation to get a number of factors bigger or smaller than the number of factors obtained in the initial extraction by principal components, as a way to show the validity of a questionnaire. For example, obtaining only ...