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Comparative research involving consensually non-monogamous (CNM) relationships and outcomes related to well-being continues to grow as an area of interest within sexual science. However, claims of sameness and/or difference between groups rely on two critical, yet widely under-appreciated assumptions: that the concepts being compared between groups are the same (i.e., measurement invariance), and that logically and statistically coherent procedures are used for evaluating sameness (i.e., equivalence testing). We evaluated the state of measurement invariance and equivalence across three studies, involving different types of CNM comparisons (i.e., relationship types, partner types) and designs (analysis of primary individual data, primary dyadic data, and secondary data). Our invariance tests of CNM compared to monogamous individuals (Study 1) and "primary" compared to "secondary" partners in dyadic appraisal of CNM individuals (Study 2) revealed that many measures of well-being failed to replicate their measurement models and were not generalizable across relationship types or partner types. Our reanalyses of existing comparative CNM effects using individual and meta-analyzed equivalence tests (Study 3), meanwhile, indicated that this literature requires more consistent reporting practices and larger samples, as most studies produced uninformative tests of equivalence. Our results illustrate the importance of auxiliary hypothesis evaluation and statistical procedure selection for generating informative comparative tests. Our findings also highlight potential divergences in social construction of well-being. We offer suggestions for researchers, reviewers, and editors in terms of needed methodological reforms for future comparative CNM research. [ABSTRACT FROM AUTHOR]