Previous research has shown that two heads working together can outperform one working alone, but whether such benefits result from social interaction or from the statistical facilitation of independent responses is not clear. Here we apply Miller's (Cognitive Psychology, 14, 247-279, 1982; Ulrich, Miller & Schröter, Behavior Research Methods, 39(2), 291-302, 2007) race model inequality (RMI) to distinguish between these two possibilities. Pairs of participants completed a visual enumeration task, both as independent individuals and as two members of a team. The results showed that team performance exceeded the efficiency of two individuals working independently, indicating that interpersonal interaction underlies the collaborative gains in this task. This interpretation was bolstered by analyses showing that the magnitude of the collaborative benefit was positively mediated by the strength of social affiliation and by the similarity of verbal communication among team members. This research serves as a proof-of-concept that Miller's RMI can differentiate between interactive versus independent effects of collaborative cognition. Moreover, the finding that social affiliation and communication similarity each contribute to the collaborative benefit suggests new avenues of research for establishing the mechanisms supporting collaborative cognition.