Advocates of performance tests of achievement sometimes contend that t
he validity of such tests typically is higher than that of multiple-ch
oice tests, despite the lower reliability of the performance measures.
This contention appears to contradict a deduction from classical test
theory and to deny the oft-quoted principle that the reliability of a
measure places an upper limit on its validity. Is this claim, therefo
re, a theoretical impossibility? In this article it is demonstrated th
at this ''anomaly'' can occur, even when the evidence of validity take
s the form of a correlation with an acceptable criterion. Whether clea
r-cut empirical examples actually can be found is an open question.