The Conception and Measurement of Asymmetric Monotonic Relationships in Sociology

Theoretical propositions in sociology are frequently stated in a form such as "the greater the A, the greater the B," which implies only monotonic relationships. Appropriate indexes are seldom used to test this type of propositions since those available are either too stringer (linear correlation, for example) or they ignore monotonicity altogheter (e.g.,x). This paper discusses two types of asymmetric monotonic indexes using a proportional reduction in error logic; one based on and one based on the correlation ratio. Weak, intermediate, and strong forms of the -type indexes are developed (two of which are currently in the literature), a general equation for the three is provided, and criteria for choosing relatively weak or strong measures are discussed. The index based on the correlation ratio agrees closely with the -type indexes (for ordinally treated interval level data) but possesses the advantage of relating directly to analysis of variance significance tests. The form of tests for all indexes is indicated.