Common Persons Design in Score Equating: A Monte Carlo Investigation

The Common Persons (CP) equating design offers critical advantages for high-security testing contexts-eliminating anchor item exposure risks while accommodating non-equivalent groups-yet few studies have systematically examined how CP characteristics influence equating accuracy, and the field still lacks clear implementation guidelines. Addressing this gap, this comprehensive Monte Carlo simulation (<i>N</i> = 5,000 examinees per form; 500 replications) evaluates CP equating by manipulating 8 factors: test length, difficulty shift, ability dispersion, correlation between test forms and CP characteristics. Four equating methods (identity, IRT true-score, linear, equipercentile) were compared using normalized RMSE and %Bias. Key findings reveal: (a) when the CP sample size reaches at least 30, CP sample properties exert negligible influence on accuracy, challenging assumptions about distributional representativeness; (b) Test factors dominate outcomes-difficulty shifts ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Δ</mml:mi> <mml:msub><mml:mrow><mml:mi>δ</mml:mi></mml:mrow> <mml:mrow><mml:mi>XY</mml:mi></mml:mrow> </mml:msub> </mml:mrow> </mml:math> = 1) degrade IRT precision severely (|%Bias| >22% vs. linear/equipercentile's |%Bias| <1.5%), while longer tests reduce NRMSE and wider ability dispersion ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub><mml:mrow><mml:mi>σ</mml:mi></mml:mrow> <mml:mrow><mml:mi>θ</mml:mi></mml:mrow> </mml:msub> </mml:mrow> </mml:math> = 1) enhances precision through improved person-item targeting; (c) Equipercentile and linear methods demonstrate superior robustness under form differences. We establish minimum operational thresholds: ≥30 CPs covering the score range suffice for precise equating. These results provide an evidence-based framework for CP implementation by systematically examining multiple manipulated factors, resolving security-vs-accuracy tradeoffs in high-stakes equating (e.g., credentialing exams) and enabling novel solutions like synthetic respondents.