title: A mathematical theory of ability measure based on partial credit item responses.
abstract: This paper defines a measure of examinees' abilities using additivity, the fundamental property of a measure, based on the partially-credited item responses. The fundamental properties of this newly-defined ability measure are demonstrated using mathematical proofs. This paper also shows that interactive ability and conditional ability are measurable with additivity. Finally, the paper looks at the ability measures associated with subscales and their decompositions.
authors.affiliation: Nan L. Kong, 270 Hampshire Dr., Plainsboro, NJ 08536, USA, nkong.usa@gmail.com.
authors.forename: Nan L
authors.initials: NL
authors.lastname: Kong
mesh_terms: D006801:Humans; D055641:Mathematical Concepts; D008962:Models, Theoretical; D011361:Professional Competence / Q000706:statistics & numerical data