Online courses can feel isolating and sometimes lack human connections that can motivate students. We developed a fully online geoscience course to build a 'Community of Inquiry' with attention to cognitive, social, and teaching presences. We ran the course using nearly identical materials for 8 semesters (recorded video lectures, labs, assignments, and assessments). Slight variations in instructor behavior caused profound impacts on student performance, creating a natural experiment to isolate factors that influence student performance. During semesters that instructors sent fewer course announcements and provided less feedback to students, about 50% more students earned D's and F's than semesters with frequent interactions. These performance drops correlated with drops in key indicators of social presence such as the number of students who thought the instructor knew their name. We developed an instrument to quantify student perceptions about the strength of student-student and instructor-student connections. An exploratory principal component analysis revealed two underlying constructs that we interpret as social presence and cognitive presence. We found that students with the highest reported social and cognitive presences had overall course grades an average of 12 points higher (out of 100) than those with the lowest presences, when all other factors were equal. Social and cognitive presence had relatively equal effects, but each explained more than 3 times the variance in student performance than the amount of time students reported spending on the course. When instructors build a supportive community with online students and facilitate their interaction around course ideas, student performance benefits.