Difficulty scaling of recognition items

Usual system: take as scale value the normal deviate corresponding to the areap = (p –p ₀)/(1 –p ₀), wherep is the proportion of correct answers andp ₀ is the chance proportion. Ifp p ₀, the item difficulty is unscalable. Proposed system: take as scale value the normal deviate corresponding to the areap =p ^x , withx so chosen thatp = .5 whenp is half-way betweenp ₀ and 1. Table givesD (=500 + 100z) forp = .00(.01)1.00 and for (= number of alternatives) 2,3,4,5,6,7, .