Using the Circular Equating Paradigm for Comparison of Linear Equating Models

Abstract

Equating error was estimated using the same test by three linear equating methods in three paradigms: (1) single-link equating of a test to itself, in which a test was administered on two different dates and the later administration was equated to the earlier adminis tration ; (2) circular equating through a chain, start ing and ending at the same test; and (3) pseudo-circular equating, in which a test was equated to itself as in the first approach through equating chains contain ing a different number of links as in the second ap proach. The mean difference between the actual scores and the equated scores, as well as the root mean square of this difference, were used as the criterion measures for equating error. The results suggested a superiority of the Tucker method for the conventional circular equating chain, and the Levine and vci methods yielded smaller errors in about half the equating chains for the pseudo-circular chain. Unexpectedly, there was not found to be a clear relationship between the num ber of links in the equating chain and the resulting error.