Common Persons Design in Score Equating: A Monte Carlo Investigation
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| Title: | Common Persons Design in Score Equating: A Monte Carlo Investigation |
|---|---|
| Language: | English |
| Authors: | Jiayi Liu, Zhehan Jiang, Tianpeng Zheng, Yuting Han (ORCID |
| Source: | Educational and Psychological Measurement. 2026 86(2):320-344. |
| Availability: | SAGE Publications. 2455 Teller Road, Thousand Oaks, CA 91320. Tel: 800-818-7243; Tel: 805-499-9774; Fax: 800-583-2665; e-mail: journals@sagepub.com; Web site: https://sagepub.com |
| Peer Reviewed: | Y |
| Page Count: | 25 |
| Publication Date: | 2026 |
| Document Type: | Journal Articles Reports - Research |
| Descriptors: | Equated Scores, Accuracy, Test Length, Difficulty Level, Correlation, Test Items, Item Response Theory, Ability, Statistical Analysis, Statistical Bias |
| DOI: | 10.1177/00131644251380585 |
| ISSN: | 0013-1644 1552-3888 |
| Abstract: | 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 (N = 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 (ΔδXY= 1) degrade IRT precision severely (|%Bias| >22% vs. linear/equipercentile's |%Bias| <1.5%), while longer tests reduce NRMSE and wider ability dispersion (σθ= 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. |
| Abstractor: | As Provided |
| Entry Date: | 2026 |
| Accession Number: | EJ1517664 |
| Database: | ERIC |
| Abstract: | 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 (N = 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 (ΔδXY= 1) degrade IRT precision severely (|%Bias| >22% vs. linear/equipercentile's |%Bias| <1.5%), while longer tests reduce NRMSE and wider ability dispersion (σθ= 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. |
|---|---|
| ISSN: | 0013-1644 1552-3888 |
| DOI: | 10.1177/00131644251380585 |
