An Evaluation of Different Statistical Targets for Assembling Parallel Forms in Item Response Theory

Abstract

Assembly of parallel forms is an important step in the test development process. Therefore, choosing a suitable theoretical framework to generate well-defined test specifications is critical. The performance of different statistical targets of test specifications using the test characteristic curve (TCC) and the test information function (TIF) was investigated. Test length, the number of test forms, and content specifications are considered as well. The TCC target results in forms that are parallel in difficulty, but not necessarily in terms of precision. Vice versa, test forms created using a TIF target are parallel in terms of precision, but not necessarily in terms of difficulty. As sometimes the focus is either on TIF or TCC, differences in either difficulty or precision can arise. Differences in difficulty can be mitigated by equating, but differences in precision cannot. In a series of simulations using a real item bank, the two-parameter logistic model, and mixed integer linear programming for automated test assembly, these differences were found to be quite substantial. When both TIF and TCC are combined into one target with manipulation to relative importance, these differences can be made to disappear.