The stability of IRT parameters under several test equating conditions

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Test equating is essential for comparing results across different test forms.
• Anchor items are commonly used to link test forms, but research on equating quality is limited.
• Previous studies often focused on absolute parameter deviations, neglecting correlations relevant for test fairness.

Purpose of the Study:

• To investigate the impact of various factors on test equating quality using a simulation study.
• To evaluate the correlation and recovery of Item Response Theory (IRT) parameters under different conditions.
• To provide insights for improving the validity and fairness of test equating.

Main Methods:

• Simulated test equating using three IRT parameters (discrimination, difficulty, ability).
• Varied equating methods, IRT models (2PL, 3PL), guessing probabilities, anchor item proportion, test set size, and anchor item discrimination.
• Assessed equating quality with sample sizes ranging from 25 to 1,000 individuals.

Main Results:

• Low guessing probabilities and high anchor item discrimination significantly improved equating quality.
• Parameter recovery increased with larger test set sizes and anchor item proportions.
• Sample sizes below 100 were inadequate; 100 or 500 individuals were justifiable but carried risks.

Conclusions:

• Distractor-free formats, high discrimination anchor items, and large samples are vital for valid test equating.
• Findings offer guidance for researchers and test developers on optimizing equating procedures.
• A comprehensive dataset and simulation guide are provided for practical application.