Two approaches, the minimax approach and the Rasch procedure, are described for the simultaneous determination of passing scores for subtests when the passing score for the total test is known. (Author/LMO)

Each Rasch (Masters) partial credit item can be expressed as the sum of independent Rasch binary items and Rasch (or Masters) indecomposable trinary items. If each trinary item is then expressed as the sum of two binary items, the binary items are positively dependent and cannot be both Rasch types. (SLD)

Given a Masters partial credit item with n known step difficulties, conditions are stated for the existence of a set of (locally) independent Rasch binary items such that their raw score and the partial credit raw score have identical probability density functions. (Author/SLD)

Procedures based on latent trait models and the Rasch model are described for computation and asymptotic statistical inference for two decision consistency indexes often used in mastery or competence testing. Simulations were conducted for typical mastery testing situations to illustrate the procedures. (SLD)