It has often been asserted that the reliability of a measure places an upper limit on its validity. This article demonstrates in theory that validity can rise when reliability declines, even when validity evidence is a correlation with an acceptable criterion. Whether empirical examples can actually be found is an open question. (SLD)

The binomial error model includes form-to-form difficulty differences as error variance and leads to Ruder-Richardson formula 21 as an estimate of reliability. If the form-to-form component is removed from the estimate of error variance, the binomial model leads to KR 20 as the reliability estimate. (Author/BW)

The reliabilities of two types of measurement plans were compared across six hypothetical distributions of true scores or abilities. The measurement plans were: (1) fixed-length, where the number of trials for all examinees is set in advance; and (2) trials-to-criterion, where examinees must keep trying until they complete a given number of trials…