Literature has suggested numerous benefits of online learning. In this study, we focused on asynchronous online discussion in higher education. We defined effective online discussions as making social presence known and conducting multidimensional discussions. Three dimensions were used to define multidimensional discussions: time, learning space, and example. Discussion posts and course evaluations made by graduate students in two online courses were examined to understand whether different sizes of online discussion groups and requirements for discussions can generate different frequencies of social presence and multidimensional discussions. Results showed that when the class size was around 30, whole class interaction in online discussions and requiring students to reply to others' posts encouraged students to make their social presence known and to conduct multidimensional discussions. Furthermore, when students were assigned to small groups of three or four students for online discussions, the frequencies of social presence and multidimensional discussions depended on other group members' engagement in discussions. Findings from the study also provided evidence that making one's social presence known was positively related to multidimensional discussions. Implications of the findings are discussed.