Design a study using the Regression Discontinuity Design (RDD) to evaluate the impact of a scholarship program on student performance.

Thank you for presenting such a thought-provoking question. It's a great opportunity to delve into how a Regression Discontinuity Design (RDD) can be effectively utilized to evaluate causal relationships, particularly in the context of assessing the impact of a scholarship program on student performance. Let's start by clarifying our approach and assumptions, and then move into the specifics of the study design. Firstly, the essence of RDD lies in its ability to approximate the experimental design in situations where random assignment is not feasible, by exploiting a predetermined cutoff point to assign treatment to observations. In our case, the treatment is the scholarship program, and the observations are student performance metrics. The selection of the cutoff score is crucial; it must be both justifiable and relevant to the scholarship criteria...