Instruction: Outline the key elements of your study design, including the selection of the cutoff score, assignment of treatment, and the statistical methods for estimating the causal effect.
Context: This question evaluates the candidate's ability to apply the Regression Discontinuity Design in a practical scenario. Candidates must demonstrate understanding of how to appropriately set a cutoff point for treatment assignment, manage potential discontinuities, and use RDD to estimate causal effects accurately while addressing any potential confounding factors.
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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. For instance, if the scholarship is intended for students demonstrating financial need and academic potential, the cutoff could be set based on a composite score that includes family income and GPA.
Now, concerning the assignment of treatment, students whose scores fall precisely at or above the cutoff would receive the scholarship, while those below would not. This binary assignment based on the score introduces a discontinuity at the cutoff point,...