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Evaluating Different Equating Setups in the Continuous Item Pool Calibration for Computerized Adaptive Testing.

Sebastian Born1, Aron Fink2, Christian Spoden3

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|June 28, 2019
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Summary

This study evaluated equating methods for computerized adaptive testing using the continuous calibration strategy (CCS). Characteristic curve methods, specifically Stocking-Lord, showed better performance for equating quality in CCS applications.

Keywords:
computerized adaptive testcontinuous calibrationequatingitem response theorysimulation

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Area of Science:

  • Psychometrics and Educational Measurement
  • Computerized Adaptive Testing (CAT)
  • Statistical Modeling in Testing

Background:

  • Digitalization offers innovative assessment opportunities, particularly in computerized adaptive testing (CAT).
  • The continuous calibration strategy (CCS) enables CAT construction without separate calibration studies.
  • Equating is critical for CCS to maintain a common metric across test cycles, relying on common items and scale transformation methods.

Purpose of the Study:

  • To evaluate different equating setups within the novel continuous calibration strategy (CCS).
  • To assess the impact of equating on item parameter estimation precision and equating quality.
  • To provide practical recommendations for CCS implementation based on simulation results.

Main Methods:

  • A Monte Carlo simulation study was conducted to examine equating setups in CCS.
  • Factors investigated included common item difficulty distribution (bimodal, normal, uniform), scale transformation method (mean/mean, mean/sigma, Haebara, Stocking-Lord), and sample size (50, 100, 300).
  • Equating quality was assessed using proportion of feasible equatings, proportion of drifted items, and error of transformation constants.

Main Results:

  • Item parameter estimation precision improved with larger sample sizes per test cycle.
  • Common item difficulty distribution and scale transformation method had no substantial impact on precision.
  • Moment methods (mean/mean, mean/sigma) resulted in extreme errors for transformation constants; characteristic curve methods (Haebara, Stocking-Lord) performed better, with Stocking-Lord showing slightly superior results.

Conclusions:

  • Increasing sample size enhances item parameter estimation in CCS.
  • Characteristic curve methods are recommended over moment methods for scale transformation within CCS.
  • The Stocking-Lord method demonstrated slightly better performance for equating quality in the CCS framework.