Common Persons Design in Score Equating: A Monte Carlo Investigation

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Common Persons (CP) equating offers advantages for high-security testing by mitigating anchor item exposure and accommodating non-equivalent groups.
• Limited research exists on how CP characteristics affect equating accuracy and implementation guidelines are scarce.

Purpose of the Study:

• To systematically examine the influence of CP characteristics and test design factors on equating accuracy.
• To provide evidence-based guidelines for implementing CP equating in high-stakes testing contexts.

Main Methods:

• A comprehensive Monte Carlo simulation with 5,000 examinees per form and 500 replications.
• Manipulation of 8 factors including test length, difficulty shift, ability dispersion, and correlation between test forms.
• Comparison of four equating methods (identity, IRT true-score, linear, equipercentile) using normalized RMSE and %Bias.

Main Results:

• CP sample size of at least 30 CPs minimizes the influence of sample properties on equating accuracy.
• Test difficulty shifts significantly degrade IRT precision, while longer tests and wider ability dispersion enhance accuracy.
• Linear and equipercentile equating methods show superior robustness when test forms differ.

Conclusions:

• A minimum of 30 CPs covering the score range is sufficient for precise equating.
• Test factors, particularly difficulty shifts, are critical determinants of equating accuracy.
• The study provides a framework for balancing security and accuracy in high-stakes equating using CP designs.