The simplified version of the Dorans and Holland (2000) measure of population invariance, the root mean square difference (RMSD), is used to explore the degree of dependence of linking functions on the Law School Admission Test (LSAT) subpopulations defined by examinees' gender, ethnic background, geographic region, law school application status, and law school admission status. Equating parallel measures of equal reliability shows very little evidence of population dependence of equating functions. When linking parallel measures, the actual amount of reliability does not seem to be a significant factor for tests with sufficient reliability. Linking two nonstrictly parallel tests that measure the same construct results in less population sensitivity than linking two tests that measure different constructs. The latter linkage leads to substantial population dependence. Linking functions are the least invariant across the ethnic subpopulations. Differences in constructs seem to play a bigger role in population sensitivity of linking functions than do differences in reliability. (Contains 14 figures and 1 table.)