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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 0000-0001-7604-9802), Shicong Feng
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: 20260101
Accession Number: EJ1517664
Database: ERIC
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  Data: Common Persons Design in Score Equating: A Monte Carlo Investigation
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  Data: 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
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  Data: 10.1177/00131644251380585
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  Data: 0013-1644&lt;br /&gt;1552-3888
– Name: Abstract
  Label: Abstract
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  Data: 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| &gt;22% vs. linear/equipercentile&#39;s |%Bias| &lt;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.
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  Data: 20260101
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  Data: EJ1517664
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        Value: 10.1177/00131644251380585
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      – SubjectFull: Accuracy
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      – SubjectFull: Test Length
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      – TitleFull: Common Persons Design in Score Equating: A Monte Carlo Investigation
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