Local Observed-Score Equating

One of the highlights in the observed-score equating literature is a theorem by Lord in his 1980 monograph, Applications of Item Response Theory to Practical Testing Problems. The theorem states that observed scores on two different tests cannot be equated unless the scores are perfectly reliable or the forms are strictly parallel (Lord, 1980, Chapter 13, Theorem 13.3.1). Because the first condition is impossible and equating under the second condition is unnecessary, the theorem is rather sobering.