Research examining oxytocin and vasopressin in humans has the potential to elucidate neurobiological mechanisms underlying human sociality that have been previously unknown or not well characterized. A primary goal of this work is to increase our knowledge about neurodevelopmental and psychiatric disorders characterized by impairments in social cognition. However, years of research highlighting wide-ranging effects of, in particular, intranasal oxytocin administration have been tempered as the fields of psychology, neuroscience, and other disciplines have been addressing concerns over the reproducibility and validity of research findings. We present a series of behavioral tasks that were conducted using a randomized, double-blind, placebo controlled, between-subjects design, in which our research group found no main effects of oxytocin and vasopressin on a host of social outcomes. In addition to null hypothesis significance testing, we implemented equivalence testing and Bayesian hypothesis testing to examine the sensitivity of our findings. These analyses indicated that 47–83% of our results (depending on the method of post-hoc analysis) had enough sensitivity to detect the absence of a main effect. Our results add to evidence that intranasal oxytocin may have a more limited direct effect on human social processes than initially assumed and suggest that the direct effects of intranasal vasopressin may be similarly limited. Randomized controlled trial registration: NCT01680718.