This paper demonstrates that the Roll and Ross (RR) and other previously published tests of the APT are subject to several basic limitations. There is a general nonequivalence of factor analyzing small groups of securities and factor analyzing a group of securities sufficiently large for the APT model to hold. It is found that as one increases the number of securities, the number of “factors” determined increases. This increase in the number of “factors” with larger groups of securities cannot readily be explained by a distinction between “priced” and “nonpriced” risk factors as it is impermissible to carry out tests on whether a given “risk factor is priced” using factor analytic procedures.