Use of rank order data in functional measurement.

Abstract

Subjects estimated average value of angle pairs using magnitude estimations or graphic ratings. These numerical response data follow a simple averaging model. Functional scaling yields a linear relation between subjective and objective angle. The numerical data are then reduced to rank orders, and J. B. Kruskal's monotone analysis of variance (MONANOVA) procedure is applied. This allows a reconstruction of the original metric information from the strictly ordinal information, illustrating the power of MONANOVA in scaling. Limitations of MONANOVA in testing the underlying model are discussed.