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Investigating the Effectiveness of a Synthetic Linking Function on Small Sample Equating

Kim, Sooyeon; von Davier, Alina A.; Haberman, Shelby J.
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Report Number:
ETS Research Report
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Subject/Key Words:
Linking Bias, Standard Error of Equating, Synthetic Function


The synthetic function, which is a weighted average of the identity (the trivial linking function for forms that are known to be completely parallel) and a traditional equating method, has been proposed as an alternative for performing linking with very small samples (Kim, von Davier, & Haberman, 2006). The purpose of the present study was to investigate the benefits of the synthetic function using various real data sets gathered from different administrations of tests from a licensure testing program. We investigated the chained linear, Tucker, Levine, and mean equating methods, along with the identity and the synthetic functions with small samples (N = 19 to 70). Neither the identity not the synthetic functions worked as well as did other linear equating methods, because test forms differed markedly in difficulty. The synthetic function cannot be used as a solution or methodological fix to a problem that is caused by poor data collection design.

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