Some Results of Ordering Theory for Guttman Scaling

Abstract

Some of the ramifications of the linear order assumption underlying much of measurement theory are discussed. Ordering theory is then described as an alternative deterministic measurement model that does not make the linear order assumption. With this theory which emanates from Guttman's scalogram analysis, one can examine the ordering properties of sets of test items. One finding of ordering theory for Guttman scaling is that the probability of four or more items forming a Guttman scale is very small. Another finding of ordering theory is that the range of Guttman scales possible for a set of n items is between I and either C(n, n/2) if n is even or C(n, n+1/2) if n is odd. A third finding of ordering theory is that Guttman scales can be classified according to a certain matrix decomposition method.