Evaluating complex educational systems with quadratic assignment problem and exponential random graph model methods

Abstract

This chapter has three objectives: (1) to describe how social network analyses (SNA) can be used to explore complexity dynamics in education; (2) to provide a primer on SNA methods; and (3) to explore statistical procedures for hypothesis testing with SNA. SNA has experienced increasing popularity in recent years, but resources available to researchers wanting to learn about this methodology are sparse. That which is available typically fails to link SNA to complexity theory, although this would seem an obvious context. This chapter briefly describes major principles of complexity theory and how network analyses are useful for exploring social dynamics. We then explain what SNA is, the types of analyses it performs, and its various uses. This section delves into issues such as designing SNA analyses, data collection procedures, and converting non-matrix data for use in SNA. Lastly, the chapter describes statistical procedures for analyzing network data. In particular, we explain how to conduct multiple regression quadratic assignment procedures and p* to test hypotheses about network dynamics. Issues of using network coefficients with traditional, variable-based statistics are discussed. Examples of applicable research questions and research studies are provided to help readers formulate questions and research designs.