Maximum likelihood factor analysis provides an effective method for estimation of factor matrices and a useful test statistic in the likelihood ratio for rejection of overly simple factor models. A reliability coefficient is proposed to indicate quality of representation of interrelations among attributes in a battery by a maximum likelihood factor analysis. Usually, for a large sample of individuals or objects, the likelihood ratio statistic could indicate that an otherwise acceptable factor model does not exactly represent the interrelations among the attributes for a population. The reliability coefficient could indicate a very close representation in this case and be a better indication as to whether to accept or reject the factor solution.

A simplified proof of a lemma by Ledermann [1938], which lies at the core of the factor indeterminacy issue, is presented. It leads to a representation of an orthogonal matrix T, relating equivalent factor solutions, which is different from Ledermann's [1938] and Guttman's [1955]. T is used to evaluate bounds on the average correlation between equivalent sets of uncorrelated factors. It is found that the minimum average correlation is independent of the data.