Critical evaluation of two F-tests for selecting the number of factors in abstract factor analysis

Two recently introduced F-tests conducted by Malinowsky and Sindreu et al. for selecting the number of factors in abstract factor analysis are critically evaluated. The first objective of this paper is to investigate the correct number of degrees of freedom to be used in these tests. It is shown that the number of degrees of freedom employed in these tests is inconsistent with the F-ratio scrutinized for significance. A modification of the degrees of freedom is proposed that yields markedly improved significance levels for the first F-test. The latter F-test can not be corrected in this way since it also violates the prerequisite of an F-test that the variances to be compared should be independent. The second objective of this paper is to demonstrate that an incorrect method does not necessarily give bad results. This phenomenon will often give rise to misleading interpretations in practice. Since empirical selection rules are rampant in the area of abstract factor analysis, pointing out this fact should serve as an important caveat.