Hierarchical cluster analysis and the internal structure of tests

Abstract

Hierarchical cluster analysis is shown to be an effective method for forming scales from sets of items. The number of scales to form from a particular item pool is found by testing the psychometric adequacy of each potential scale. Higher-order scales are formed when they are more adequate than their component sub-scales. It is suggested that a scale's adequacy should be assessed, by a new measure of internal consistency reliability, coefficient beta, which is defined as the worst split-half reliability of the test. Comparisons with other procedures show that hierarchical clustering algorithms using this psychometrically based decisions rule can be more useful for scale construction using large item pools than are conventional factor analytic techniques. © 1979, Taylor & Francis Group, LLC. All rights reserved.