Longitudinal predictions using alternative binning to reduce regression to the mean

Educational policies in Texas that regulate the evaluations of students, teachers, and schools, can have profound impacts on the success of those individuals and institutions. The evaluations are largely based on the outcomes from standardized exams, as well as graduation rates and college preparedness. The analysis of standardized exam scores and policy impacts must be accurate, rapid, and reliable if it is to inform new policies. The possibility of using year by year longitudinal series of exams to extract predictions about policy interventions is greatly impacted, in practice, by a statistical phenomenon known as regression to the mean. I present a novel method, inspired by statistical and fluid mechanics, to address this problem, called Alternatively Binned Streamlines. I justify the use of this method through a simple theory. Then I apply it to the Texas State Longitudinal Data System, which contains standardized testing data for primary and secondary school students between 2003 and 2015. I show that regression to the mean can largely be eliminated, making it possible to predict the longitudinal performance of aggregated students, using only two or three years of data, with acceptable accuracy. Through these predictions, I also identify the effects of a state-wide intervention called the Student Success Initiative. Thus, I demonstrate that Alternative Binning provides rapid analysis of policy impacts and predictions of longitudinal student performance with the ability to inform policy.