On the Number of Factors

A proposed criterion for the number of factors is developed on the basis of the similarity between a factorial residual and the partial correlation coefficient; something is known concerning the sampling error of the latter. Instead of computing the residuals as partials, a formula is presented for adjusting the standard deviation of the distribution of residuals so as to approximate the S.D. of the residuals as partial correlations. The criterion requires that factors be extracted until the adjusted S.D. reaches or falls below 1/√N. When tried out on six samples drawn from six universes of known factorial description, the criterion indicated the correct number of factors each time. The requisites of situations adequate for such empirical checks are discussed.