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Smoothing and Equating Methods Applied to Different Types of Test Score Distributions and Evaluated With Respect to Multiple Equating Criteria

Moses, Tim P.; Liu, Jinghua
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Report Number:
ETS Research Report
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Subject/Key Words:
Equipercentile Equating, Presmoothing, Postsmoothing, Equating Criteria


In equating research and practice, equating functions that are smooth are typically assumed to be more accurate than equating functions with irregularities. This assumption presumes that population test score distributions are relatively smooth. In this study, two examples were used to reconsider common beliefs about smoothing and equating. The first example involves a relatively smooth population test score distribution and the second example involves a population test score distribution with systematic irregularities. Various smoothing and equating methods (presmoothing, equipercentile, kernel, and postsmoothing) were compared across the two examples with respect to how well the test score distributions were reflected in the equating functions, the smoothness of the equating functions, and the standard errors of equating. The smoothing and equating methods performed more similarly in the first example than in the second example. The results of the second example illustrate that when dealing with systematically irregular test score distributions, smoothing and equating methods can be used in different ways to satisfy different equating criteria.

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