The question of trait equivalence asks whether different methods of measurement share sufficient convergent and discriminant properties and correlates to warrant interpreting their respective scores as indicators of the same tract or construct. In the present context of contrasting construction versus choice by cognitive measurement, the method difference at issue involves different item-response formats, especially multiple-choice versus completion and construction. The Traub and Snow chapters offer two perspectives on the issue of trait equivalence, namely the psychometric and the cognitive-experimental.