The purpose of this paper is to explore methods to approximate population invariance without conducting multiple linkings for subpopulations. Under the single group or equivalent groups design, no linking needs to be performed for the parallel-linear system linking functions. The unequated raw score information can be used as an approximation. For other linking functions that are nonparallel-linear, linking only needs to be conducted for the total population. The difference of the standardized mean differences between each subpopulation and the total population across the old form and the new form can be used as an approximation of population invariance. Under the nonequivalent groups with anchor test design, conducting separate subpopulation linking and comparing them to the total population linking may still be the best way to estimate population invariance.
