A Method of Scalogram Analysis Using Summary Statistics
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TL;DR
A method of Guttman scalogram analysis is presented that does not involve sorting and rearranging the entries in the item response matrix and several methods are suggested for dealing with non-dichotomous items.
Abstract
A method of Guttman scalogram analysis is presented that does not involve sorting and rearranging the entries in the item response matrix. The method requires dichotomous items. Formulas are presented for estimating the reproducibility of the scale and estimating the expected value of the chance reproducibility. An index of consistency is suggested for evaluating the reproducibility. An illustrative example is presented in detail. The logical basis of the method is discussed. Finally, several methods are suggested for dealing with non-dichotomous items.