Popular measurement invariance testing procedures for latent constructs evaluated by multiple indicators in distinct populations are revisited and discussed. A frequently used test of factor loading invariance is shown to possess serious limitations that in general preclude it from accomplishing its goal of ascertaining this invariance. A process of mean intercept invariance evaluation is subsequently examined, and it is indicated that within this framework there is no statistical test available for group identity in them. Rather than pursuing these popular and widely used invariance testing procedures, it is recommended that empirical studies on constructs in multiple populations be concerned in general with alternative measurement invariance examination and ensuring the inclusion of their invariance conditions in models aimed at investigating group differences and similarities in latent means, variances, and interrelationships. The discussion is illustrated using data from a cognitive intervention study. (Contains 4 notes and 1 table.)