Effectiveness of the hybrid Levine equipercentile and modified frequency estimation equating methods under the common-item nonequivalent groups design

The purpose of this study was to evaluate the effectiveness of the hybrid Levine equipercentile (Hybrid LE) and modified frequency estimation (MFE) equating methods in improving accuracy of equating as compared to the percentile rank frequency estimation (FE), kernel frequency estimation (Kernel FE) and percentile rank chained equipercentile (CE) equating methods under the common-item nonequivalent groups (CINEG) design. The methods were compared under a wide variety of simulated conditions with log-linear pre-smoothing. The simulated conditions reflected differences in sample size, group proficiency, test length, ratio of common items and the similarity of form difficulty. An item response theory (IRT) model was used to define the "true" equating criterion, simulate group differences, and generate response data.

Considered collectively, the simulation results revealed that the Hybrid LE and MFE methods performed best under most simulation conditions. When group proficiency differed only in the mean, the MFE method produced the lowest equating error. When the group proficiency differed in both mean and variance, the Hybrid LE method yielded the lowest error. Overall, the Hybrid LE method yielded less bias but greater standard error of equating (SEE) than the MFE method except at the two ends of the scale score. Aside from method effects, group proficiency differences had the most impact on equating error. Equating error also decreased as the common item ratio increased, sample size increased and test length decreased. Form difficulty, in contrast, had little effect on equating error.