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Examining Potential Boundary Bias Effects in Kernel Smoothing on Equating: An Introduction for the Adaptive and
Jaime A Cid1, Alina A von Davier1
1Educational Testing Service, Princeton, NJ, USA.
Kernel equating (KE) can be biased by extreme scores. This study explores atypical score effects on KE and introduces Epanechnikov and adaptive kernels to reduce boundary bias in test score equating.
Area of Science:
- Psychometrics
- Educational Measurement
- Statistical Modeling
Background:
- Test equating ensures comparability across different test forms.
- Kernel equating (KE) uses Gaussian kernel smoothing for score distribution continuization.
- Boundary bias in KE may arise from smaller sample sizes at score distribution endpoints.
Purpose of the Study:
- Investigate the impact of extreme scores (spikes) on KE with asymmetric distributions.
- Evaluate alternative kernels (Epanechnikov, adaptive) to mitigate boundary bias in smoothing.
Main Methods:
- Simulated observed scores using the beta-binomial model for skewed distributions.
- Employed the randomly equivalent groups equating design (Study I).
- Introduced Epanechnikov and adaptive kernels (Study II).
Main Results:
- Atypical scores at distribution extremes can affect KE results.
- Epanechnikov and adaptive kernels show potential for reducing boundary bias.
Conclusions:
- The choice of kernel and handling of extreme scores are critical in test equating.
- Alternative kernels offer promising solutions for improving the accuracy of KE.
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