In order to determine whether or not an effect/association is absent based on a statistical test, the recommended frequentist tool is the equivalence test. In this talk, we review three recent and related papers. First, we introduce non-inferiority tests (one-sided equivalence tests) for ANOVA and linear regression analyses that correspond to standard F-tests for η̂2 and R2 (https://arxiv.org/abs/1905.11875). Second, with the aim of motivating a critical discussion as to what is acceptable and desirable in the interpretation of equivalence tests, we consider a series of controversial scenarios in which the equivalence margin is defined post-hoc (https://arxiv.org/abs/1807.03413). Finally, we propose an alternative publication policy similar to "Registered Reports" that incorporates equivalence testing in order to strategically reduce publication bias (https://doi.org/10.1371/journal.pone.0195145).