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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

On mean-sigma estimators and bias.

Peter Baldwin¹

¹National Board of Medical Examiners, Philadelphia, PA 19104-3102, USA. pbaldwin@nbme.org

The British Journal of Mathematical and Statistical Psychology

|May 11, 2012

Summary

The mean-sigma method for equating test forms using item response theory (IRT) can produce biased results. This bias in transformation constants is inherent and depends on factors like the number and quality of anchor items.

Area of Science:

Psychometrics
Educational Measurement
Item Response Theory

Background:

Equating test forms is crucial for comparing scores across different assessments.
Item Response Theory (IRT) is a common framework for test analysis.
The mean-sigma method is a standard procedure for linear test equating when common items are present.

Purpose of the Study:

To investigate the accuracy of the mean-sigma method for estimating linear transformation constants in IRT.
To determine if the mean-sigma estimators are biased when equating two test forms.

Main Methods:

Analytical derivation of transformation constants.
A small-scale simulation study to empirically assess bias.

Main Results:

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The mean-sigma estimators for transformation constants were found to be biased.
The bias was systematic, though modest relative to random error in the studied conditions.
The magnitude of the bias was influenced by the number of anchor items and the precision of their difficulty estimates.

Conclusions:

The mean-sigma method is not perfectly accurate for equating test forms under IRT.
Researchers should be aware of potential bias when using this method.
Test design features, such as anchor item selection and quality, impact equating accuracy.