Difficulty Scaling of Recognition Items

Abstract

Usual system: take as scale value the normal deviate corresponding to the area p″ = (p − p₀)/(1 − p₀), where p is the proportion of correct answers and p₀ is the chance proportion. If p ≦ p₀, the item difficulty is unscalable. Proposed system: take as scale value the normal deviate corresponding to the area p′ = p^x, with x so chosen that p′ = .5 when p is half-way between p₀ and 1. Table gives D (=500 + 100z) for p = .00(.01)1.00 and for a (= number of alternatives) 2,3,4,5,6,7, ∞.