Asymptotic and Sampling-Based Standard Errors for Two Population Invariance Measures in the Linear Equating Case

Abstract

This article describes two methods for obtaining the standard errors of two commonly used population invariance measures of equating functions: the root mean square difference of the subpopulation equating functions from the overall equating function and the root expected mean square difference. The delta method relies on an analytical approximation and provides asymptotic standard errors, whereas the grouped jackknife method is a sampling-based method. The expressions for the delta method are presented for the linear equating function. Both methods were applied to a real data application. The results indicate little difference between the standard errors found by the two methods.