Observed-score equating as a test assembly problem

Abstract

A set of linear conditions on the item response functions is derived that guarantees identical observed-score distributions on two test forms. The conditions can be added as constraints to a linear programming model for test assembly that assembles a new test form to have an observed-score distribution optimally equated to the distribution of the old form. For a well-designed item pool, use of the model results into observed-score pre-equating and prevents the necessity of post hoc equating by a conventional observed-score equating method. An empirical example illustrates the use of the model for an item pool from the Law School Admission Test (LSAT). (Contains 6 figures and 33 references.) (Author/SLD) ******************************************************************************** Reproductions supplied by EDRS are the best that can be made from the original document. *******************************************************************************

Computerized Adaptive Testing with Equated Number-Correct Scoring

“…. , n. Van der Linden & Luecht (1998) proved that, for any common distribution h(θ ), the distributions of X and Y are identical if and only if…”

“…The constraints are derived from a set of conditions on the IRFs that guarantees that the NC score distributions on two test forms will be identical (van der Linden & Luecht, 1998). To impose the item selection constraints, the method of constrained CAT with shadow tests (van der Linden, 2000a; van der Linden & Reese, 1998) is used.…”

“…As a result, the CAT NC scores also are equated across administrations. The constraints are derived from van der Linden & Luecht's (1998) set of conditions on item response functions that guarantees identical observed NC score distributions on two test forms. An item bank from the Law School Admission Test was used to compare the results of the algorithm with those for equipercentile observed-score equating, as well as the prediction of NC scores on a reference test using its test response function.…”

A New Concurrent Calibration Method for Nonequivalent Group Design under Nonrandom Assignment

“…θ ij is distributed as N(μ j , σ 2 j ) (in this paper, we do not assume the multidimensionality of abilities. For the problem of multidimensionality of abilities, see van der Linden & Luecht, 1998). Under the three-parameter logistic model, the probability that the ith examinee of ability θ ij correctly answered item k of test X (X = A, B, C) is defined as…”

Weighting Test Samples in Irt Linking and Equating: Toward an Improved Sampling Design for Complex Equating

“…The objective of the study is to achieve a stable scale for an assessment with multiple forms and to explore an effective paradigm to evaluate the procedure. A future research direction is to explore a formal optimal sampling design for weighted linking and equating of multiple test forms over many administrations (Berger, 1991(Berger, , 1997Berger & van der Linden, 1992;Buyske, 2005;Lord & Wingersky, 1985;Stocking, 1990;van der Linden & Luecht, 1998).…”