Population Invariance in Equating and Linking: Concept and History

The concept of invariance in equating and linking is traced from the 1950s to the present. A number of research studies that examined population invariance are reviewed. Theory and research suggest that linkings other than equatings are population dependent. Theory also indicates that equatings are population dependent, although when test forms are built to detailed tables of content and statistical specifications and alternate forms are very similar to one another, the research suggests that equatings might be approximately population invariant. Suggestions are made about further research that should be conducted on methodology for examining population invariance and on empirical research to better understand the conditions under which equatings are sufficiently population invariant for practical purposes.