One of the fundamental requirements of equating functions is that they should be population invariant. Dorans and Holland (2000) introduced general measures for evaluating population invariance by comparing linking functions obtained on subpopulations with those obtained on the full population. Their discussion was restricted to data collection designs involving a single population. This report contains a collection of related papers from five different testing programs that use a variety of equating/linking settings, data collection designs, tests structures, and equating methods to assess the degree of invariance of subpopulation equating results from total population equating results. The measures of population invariance show promise as valuable tools for evaluating the equatability of tests. Earlier versions of these papers were presented at a symposium at the 2004 annual meeting of the National Council on Measurement in Education.