The effects of intranasal oxytocin on social cognition are mixed, with several non-significant reports casting some doubts on its efficacy. Nevertheless, drawing inferences from non-significant values is problematic as non-significant results can be indicative of either statistical equivalence or insensitive data. Equivalence tests can be used to assess evidence for statistical equivalence, which can consequently facilitate theory falsification. To improve the inference of non-significant NHST p-values, this paper reports a set of equivalence tests performed on data from a recent meta-analysis synthesizing 32 intranasal oxytocin studies. Data from 26.1% of non-significant meta-analytic effects were indicative of data insensitivity, rather than statistical equivalence. Equivalence tests were also performed on a set of previously unpublished data from one laboratory, to examine whether unpublished data yields similar outcomes. Of the 34 non-significant effects, 73.5% were due to data insensitivity. As these analyses illustrate how non-significant intranasal oxytocin results may not necessarily support the absence of an effect, researchers are encouraged to implement equivalence tests in the design of their studies. By facilitating theory falsification, the adoption of equivalence tests can advance the field by redirecting resources to more promising avenues of research.