Utilizing the Generalized Likelihood Ratio as a Termination Criterion

Computer-based testing can be used to classify examinees into mutually exclusive groups. Currently, the predominant psychometric algorithm for designing computerized classification tests (CCTs) is the sequential probability ratio test (SPRT; Reckase, 1983) based on item response theory (IRT). The SPRT has been shown to be more efficient than confidence intervals around θ estimates as a method for CCT delivery (Spray & Reckase, 1996; Rudner, 2002). More recently, it was demonstrated that the SPRT, which only uses fixed values, is less efficient than a generalized form which tests whether a given examinee’s θ is below θ1or above θ2 (Thompson, 2007). This formulation allows the indifference region to vary based on observed data. Moreover, this composite hypothesis formulation better represents the conceptual purpose of the test, which is to test whether θ is above or below the cutscore. The purpose of this study was to explore the specifications of the new generalized likelihood ratio (GLR; Huang, 2004). As with the SPRT, the efficiency of the procedure depends on the nominal error rates and the distance between θ1 and θ2 (Eggen, 1999). This study utilized a monte-carlo approach, with 10,000 examinees simulated under each condition, to evaluate differences in efficiency and accuracy due to hypothesis structure, nominal error rate, and indifference region size. The GLR was always at least as efficient as the fixed-point SPRT while maintaining equivalent levels of accuracy.