The social structure of small groups, such as families and teams, is a hot topic of research. For example, medical and public health practitioners are interested in communication and support systems in family units, while organizational and defense fields look to understand and manipulate coordination, collaboration, and leadership structures within small teams. The structure of small group networks matters. Small group research deals with small data, and specifically, small networks. Although analyzing small networks data may appear easy in the face of “big data” challenges, it also presents hard problems. Descriptions of small network structure, such as density and triad counts, is a simple task. However testing hypotheses and applying statistical models is challenging because most statistical models rely on large samples and asymptotic approximations, making the usage of these methods unfeasible with such data. From the simplest to the most complex statistical analyses, problems with small networks arise fast. For example, in the case of Exponential Random Graph Models (ERGMs), approximation-based estimation methods may not converge. Moreover, even a simple correlation between two small networks may not be defined. One approach to solving these issues is through the use of exact statistics; i.e. calculating the exact likelihood instead of the approximate one, or using hamming distances to define correlation statistics that are defined for all cases. We propose new methodological approaches for these types of problems by means of simulation-based tests and exploiting small sample sizes to compute exact statistics. We apply these new methods to data collected through a small team experiment, in which we observed collaboration and leadership networks in small teams (3 to 5 members), and assess team performance via a test for collective intelligence.
Joint work with Kayla de la Haye.