Sir: It is well known that the most applied criteria for determining the number of underlying factors from a data matrix being factor-analyzed are the Malinowski's indicator @ND) function [l] and the Wold's double cross-validation (DCV) procedure [2]. Recently, we have proposed another proof that is very straightforward and easy to handle [3]. It has been successfully
applied in real cases compared with both IND and DCV criteria. Accordingly it has been also selected for the determination of the number of factors in the program HOLMES, recently published in this Journal [4]. However, this new criterion neither has been outlined in detail nor has been assessed statically for the sake of suitability. The aim of this letter is to show to the users of factor analysis (FA) in some detail the advantages and reliability of this criterion that we called the RSD F criterion Let us assume a given data matrix X of r rows and c columns. This raw data matrix is the sum of two terms: a pure data matrix without error and an error matrix. When the pure matrix is factor-analysed in R-mode, we obtain just the true number of underlying factors, namely, f. That is, f eigenvectors and f eigenvalues. However, when the raw data matrix X is factor-analysed, we obtain c eigenvectors and c eigenvalues [l]. Only f of the c eigenvectors are associated with the true factors, and the remaining of l Corresponding author.