A Derivation of Levine's Formulae (for Equating Unequally Reliable Tests Using Random Groups) without the Assumption of Parallelism
Robert G. MacCann · Educational and Psychological Measurement · 1989
Levine's equations for random groups and unequally reliable tests can be used to equate tests X and Y through performance on an anchor test, Z. Levine's derivation assumed that all three tests were parallel in function, with X and Y of different lengths. It is shown that the parallelism requirement is unnecessary, as it is sufficient to assume only that X and Y are congeneric, an assumption that is itself implicit in the definition of linear test equating.