Tau-equivalence and equipercentile equating (Q1061444)

Test scores that are not perfectly reliable cannot be strictly equated unless they are strictly parallel [cf. \textit{F. M. Lord}, Applications of item response theory to practical testing problems. Lawrence Erlbaum Associates (1980)]. This fact implies that tau-equivalence can be lost if an equipercentile equating is applied to observed scores that are not strictly parallel. Seventy-two simulated testing conditions are produced to simulate equating tests with different difficulties and discriminations. Number-correct and trait metrics are examined. When an equipercentile equating is applied to these data, locally biased (i.e., non-tau- equivalent) results are produced for tests of unequal difficulty. Differences between the criteria of tau-equivalence and equipercentile equivalence are discussed.