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Edison M Choe1, Hua-Hua Chang2

  • 1Graduate Management Admission Council™ (GMAC™), 11921 Freedom Drive, Suite 300, Reston, VA , 20190, USA. echoe@gmac.com.

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Summary
This summary is machine-generated.

This study introduces the sampling distribution for the average test overlap rate in computerized adaptive tests (CAT). This enables better statistical comparisons and confidence intervals for test security and item pool utilization.

Keywords:
asymptotic theorycomputerized adaptive testingitem exposurepool utilizationtest overlaptest security

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Area of Science:

  • Psychometrics
  • Educational Measurement
  • Computerized Adaptive Testing (CAT)

Background:

  • The average test overlap rate is a key metric for assessing computerized adaptive test (CAT) security and item pool usage.
  • Current understanding lacks a formal statistical distribution for this crucial measure, hindering rigorous analysis.

Purpose of the Study:

  • To derive the asymptotic sampling distribution of the average test overlap rate in fixed-length CAT.
  • To enable the estimation of standard errors and the construction of confidence intervals for this statistic.
  • To facilitate statistical comparisons between different CAT designs based on their overlap rates.

Main Methods:

  • Mathematical derivation of the asymptotic distribution for a linear transformation of the average test overlap rate.
  • A simulation study to compare average test overlap rates between two CAT designs with varying exposure control strategies.

Main Results:

  • The asymptotic distribution of the average test overlap rate in fixed-length CAT has been established.
  • Theoretical results allow for the calculation of standard errors and confidence intervals.
  • Simulation results provide a practical demonstration of comparing overlap rates across different CAT designs.

Conclusions:

  • The derived sampling distribution provides a robust statistical foundation for analyzing average test overlap rates in CAT.
  • This advancement supports more accurate assessments of test security and item pool utilization.
  • The findings facilitate evidence-based decisions in the design and implementation of CAT systems.