Number of Cases and Number of Factors: an Example Where N is Very Large

a principle components analysis with unities in the diagonal of the correlation matrix. After the number of factors has been fixed, iterations may be performed in order to estimate communalities for the number of factors selected. Kaiser’s recommendation is related to his exposition of the psychometric approach to factor analysis and factor interpretation in contrast with the statistical hypothesis testing approach. The writer is, in general, in sympathy with this point of view. He has, for example, recommended the translation of t-ratios and F-ratios into measures of relationship that reflect common variance and are independent of N. When the latter is done, however, it is still possible to estimate population values. This is not possible in factor analysis so that unthinking acceptance of the Kaiser point of view could lead to the interpretation of large factor loadings that represent nothing but chance or, on the other hand, to the discard of useful information. Even if one stresses the descriptive psychometric interpretation of factors, one might still be interested in factors having roots of less than one. Correlations of .20 for example, represent little common variance but depending upon circumstances, of which sampling sta-