Recently, it has been proposed that all non-cognitive measures of personality share a general factor of personality. A problem with many of these studies is a lack of clarity in defining a general factor. In this paper we address the multiple ways in which a general factor has been identified and argue that many of these approaches find factors that are not in fact general. Through the use of artificial examples, we show that a general factor is not:
1.
The first factor or component of a correlation or covariance matrix.
2.
The first factor resulting from a bifactor rotation or biquartimin transformation.
3.
Necessarily the result of a confirmatory factor analysis forcing a bifactor solution.
We consider how the definition of what constitutes a general factor can lead to confusion, and we will demonstrate alternative ways of estimating the general factor saturation that are more appropriate.