Accounting for structure in education assessment data using hierarchical models
As the field of education continues to grow, new methods and approaches to teaching are being developed with the goal of improving students' understanding of concepts. While research exists showing positive effects for particular teaching methods in small case studies, generalizations to larger populations of students, which are needed to adequately inform policy decisions, can be difficult when using traditional inferential procedures for group comparisons that rely on randomization, replication, and control over relevant factors.
Data collected to compare teaching methods often consists of student level responses, where students are nested within a class, which is typically the experimental unit. Further, for studies in which the scope of inference exceeds individual schools or instructors, we often have classes nested within other factors such as semesters or instructors. In the first part of this dissertation, we explore the consequences of analyzing such data without accounting for the nesting structure. We then show that a hierarchical modeling approach allows us to appropriately account for structure in this type of data. As an illustration, we demonstrate the use of a model-based approach to comparing two teaching methods by fitting a hierarchical model to data from a second course in statistics at Iowa State University.
To fit a hierarchical model to a dataset, the nesting structure must be chosen, a priori. However, with data from an educational setting, there can be instances when the nesting structure is ambiguous. For example, should semesters be nested within instructors or vice versa? In part two of this dissertation, we develop a data-driven diagnostic using moment-based variance estimators to aid in the choice of nesting structure prior to fitting a hierarchical model. We conduct a simulation study to demonstrate the diagnostic's effectiveness and then apply the diagnostic to data from a nationally recognized standardized exam measuring statistical understanding after a first course in statistics. The results from the diagnostic and the subsequent fitted hierarchical model demonstrate the presence of a difference between the upper level grouping variable that represents the effect of interest. More broadly, this example is intended to highlight the use of hierarchical models for analyzing education data in a way that adequately accounts for variation between students that arises from nested data structures.