ABSTRACT
The information function I{θ, y} for any score y is by definition inversely proportional to the square of the length of the asymptotic confidence interval for estimating ability θ from score y (Birnbaum, 1968, Section 17.7). In this chapter, an asymptotic result means a result that holds when the number n of items (not the number N of people) becomes very large. In classical test theory, it is usual to consider that a test is lengthened by adding items “like those in the test,” that is, by adding test forms that are strictly parallel (see Section 1.4) to the original test. This guarantees that an examinee's proportion-correct true score (“zayta”) ζ ≡ ξ/n is not changed by lengthening the test. We shall use lengthening in this sense here and throughout this book.
