This exploratory study was built on research spanning three decades. Petersen, Marco, and Stewart (1982) conducted a major empirical investigation of the efficacy of different equating methods. The studies reported in Dorans (1990) examined how different equating methods performed across samples selected in different ways. Recent population sensitivity studies have examined whether equating methods yield comparable results across subpopulations. The current study confirms earlier research and clarifies the role of population invariance studies in assessing equating results. A content-appropriate anchor produced solid equating results under small ability differences and divergence of equating results for different methods under large ability differences. Results showed a content-inappropriate anchor did not produce sound score equatings but did yield a strong degree of invariance. Lack of population invariance of equating results can be taken as evidence that a linking is not an equating. The existence of invariance does not mean, however, that equating has been achieved. (Contains 7 tables.)