Linear equating models for the common-item nonequivalent-populations design

Abstract

The Tucker and Levine equally reliable linear methods for test form equating in the common-item nonequivalent- populations design are formulated in a way that promotes understanding of the methods. The formulation emphasizes population notions and is used to draw attention to the practical differences between the methods. It is shown that the Levine method weights group differences more heavily than the Tucker method. A scheme for forming a synthetic population is suggested that is intended to facilitate interpretation of equating results. A procedure for displaying form and group differences is developed that also aids interpretation.