Relationships Between the Item Difficulty and Discrimination Indexes

Abstract

The dependence of the item discrimination index (D) on the item difficulty index ( p), and the relationship of D and p to the phi coefficient (ϕ) are delineated. A table of critical values of D for significance at the .10 and .05 levels, with the number of examinees in the upper group (n, ) on total test score ranging from 10 to 25 and p ranging from .10 to .90, is presented. This table may be used to determine an acceptable magnitude of D for a given p and n1 or to find whether a particular combination of p and D will yield a significant ϕ.