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Theoretical and Empirical Standard Errors for Two Population Invariance Measures in the Linear Equating Case RMSD REMSD

von Davier, Alina A.; Manalo, Jonathan; Rijmen, Frank
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Report Number:
ETS Research Report
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Subject/Key Words:
Population Invariance, Root Mean Square Difference (RMSD), Root Expected Mean Square Difference (REMSD), Jackknife Estimation, Standard Error of Measurement


The standard errors of the 2 most widely used population-invariance measures of equating functions, root mean square difference (RMSD) and root expected mean square difference (REMSD), are not derived from common equating methods such as linear equating. Consequently, it is unknown how much noise is contained in these estimates. This paper describes 2 methods for obtaining the standard errors for RMSD and REMSD. The delta method relies on an analytical approximation and provides asymptotic standard errors. The grouped jackknife method is a sampling-based method. Both methods were applied to a real data application. The results showed that there was very little difference between the standard errors found by the 2 methods.

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