Test Scores, Classroom Performance, and Capacity in Academically Selective School Program Admissions

We study the admissions problem for academically selective K-12 education programs and magnet schools. Many states and public school districts are either required by law to, or choose to, offer specialized programs for students who show potential for higher levels of accomplishment than their peers (these are often referred to as programs for gifted and talented, high achieving, or academically advanced students). Such programs have come under scrutiny for potentially enhancing underlying inequities, and the role of test scores versus other attributes in admission to these programs has in particular been called into question. We introduce a stylized model in which the population consists of advantaged and disadvantaged students, with both groups having the same true distribution of underlying potential. The advantaged population is more likely to perform well in both tests and classroom achievement, with different characteristics for how this advantage is distributed among high-achievers and low-achievers. We show that, in a group-blind model, using both test scores and classroom achievement can be useful in mitigating inequities beyond even group-aware models that apply different thresholds on one or the other. This is accompanied by an "inversion" phenomenon where in some cases the program preferentially admits students with lower classroom achievement and a high test score. We also use our model to analyze how the capacity of the magnet school or specialized program affects the distribution of outcomes between the two populations.