One common weakness in multigroup comparison research is the pervading assumption that both the assessment scale and the construct(s) it is designed to measure are operating equivalently across the groups of interest. Structural equation modeling (SEM) has long been recognized as the premier methodological approach to test assumptions of equivalence. The primary focus of this chapter is directed toward the use of SEM in testing for the equivalence (also termed “invariance”) of assessment scales across independent groups. The purposes are threefold: (a) to explicate the basic notions underlying the concepts of measurement and structural equivalence; (b) to outline and describe the hierarchical set of steps involved in testing for measurement and structural equivalence; and (c) to provide an annotated, yet concise illustration of this equivalence-testing process as it relates to a commonly used assessment scale designed to measure teacher burnout across elementary and secondary female teachers.