Washington Achievement Data Explorer (WADE): Student Performance Across WA State

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Explanation of District Residuals

Research has shown that while teachers, schools, and districts have considerable impact on student performance, an even larger percent of the variation in student test scores can be explained by student characteristics. In particular, a student’s poverty level—as measured by whether a student is eligible for free or reduced priced lunch—is highly correlated with that student’s performance on state exams. Therefore, it is important to control for the percent of students receiving free or reduced priced meals in a district to provide a more balanced comparison of district performance.

To do this, we run a regression of the percent of students who passed the state exam (separately for reading and math) on the percent of students in the district who receive free or reduced priced lunch that year1. The coefficient from this regression gives the expected change in the percent of students passing the state exam correlated with a one percent increase in the percent of students in the district eligible for free or reduced priced lunch. This coefficient is -.45 for math and -.38 for reading, meaning that, for example, an increase of 10 percentage points in the percent of students eligible for free or reduced priced lunch is correlated with a decrease of 4.5 percentage points in math and 3.8 percentage points in reading in the percent of students passing the state exam.

These regressions also produce residuals, which we use as a rough measure of district performance, because they give the difference between the percent of students we would predict to pass the state and the percent of students who actually passed the test in that grade, district, subject, and year. As a visual representation of this concept, consider hypothetical Districts A and B:

residual_explanation

Although a higher percentage of students in District A passed the state exam than in District B, the percent in District A is less than we would have predicted based on the poverty level of the district, while the percent in District B is greater than we would have predicted. The residual for each district, -8% for District A and +5% for District B, reflects this.

1The model is as follows:

model

In this regression, the dependent variable Xgjst is the percent of students in grade g, district j, subject s, and year t who passed the state exam. The dependent variables are FRPMjt, the percent of students in the district who received free or reduced priced meal in district j and year t, as well as grade (γg) and year (ϕt) fixed effects.