Hypothesis Testing for Group Structure in Legislative Networks

Scholars of social networks often rely on summary statistics to measure and compare the structures of their networks of interest. However, measuring the uncertainty inherent in these summaries can be challenging, thus making hypothesis testing for network summaries difficult. Computational and nonparametric procedures can overcome these difficulties by allowing researchers to generate reference distributions for comparison directly from their data. In this research, I demonstrate the use of nonparametric hypothesis testing in networks using the popular network summary statistic network modularity. I provide a method based on permutation testing for assessing whether a particular network modularity score is larger than a researcher might expect due to random chance. I then create a simulation study of network modularity and its simulated reference distribution that I propose. Finally, I provide an empirical example of this technique using cosponsorship networks from U.S. state legislatures.