Test Assembly

A Stochastic Search for Test Assembly, Item Pool Analysis, and Design (RR 04-01)

by Dmitry Belov, Law School Admission Council; and Ronald D. Armstrong, Rutgers, The State University of New Jersey

The problems of item pool analysis and design are the subject of many recent studies. The rationale for this type of research is to increase the usability of existing item pools and to decrease the cost of designing new items. Clearly these are crucial problems for all testing agencies.

This paper demonstrates that a stochastic search technique allows for the solution of various item pool analysis and design problems. Stochastic search refers to a family of approaches that allows for the introduction of random noise into the model and/or search strategy being developed. The problems addressed in this paper are as follows:

Comparison of two pools: Given two different item pools, identify the strengths and weaknesses of the pool characteristics from the test assembly point of view.

Constraint difficulty and relaxation: Given an item pool and test assembly constraints, identify the most difficult constraint(s), that is, the constraints that prevent the assembly of additional test forms. Explore how relaxation of those constraints impacts the number of feasible forms available from the pool.

Designing new items: Given pool and test assembly constraints, determine the properties of the items that should be added to a pool in order to acquire more test forms.

The paper employs stochastic search techniques to assemble linear standardized tests where the properties of the constraints are used to guide the search. The nature of the random search provided efficient and elegant solutions to the above problems.

The theoretical results of this paper can be used either for development of paper-and-pencil tests or computerized adaptive tests (CAT). Based on methods described in this paper, software tools were developed for assembling Law School Admission Test (LSAT) forms, extracting multiple disjoint LSAT forms, and determining the characteristics that new items to the pool should have in order to obtain additional LSAT forms from the pool.

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