IN this paper three changes and one new development for the method of exploratory factor analysis (a second generation Little Jiffy) developed by Kaiser (1970) are described. Following this short description a step-by-step computer algorithm of the revised method-dubbed Little Jiffy, Mark IV-is presented. Extensive empirical experience with &dquo;a second generation Little Jiffy&dquo; (Kaiser, 1970) indicates that the method, for large matrices, consistently mildly underfactors. A revision is called for. Thus, the writers adopt as the answer for the crucially important question of the &dquo;number of factors&dquo; Guttman’s (1954) classic weaker lower bound, the index of the covariance matrix (with zeros in the diagonal) under consideration. This answer is the same as that given by Kaiser’s (1956, 1960, 1970) extensively used &dquo;eigenvalues greater than one of R.&dquo;
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