Arnold Kling wondered aloud what the relationship would be between measures of a school district’s poverty level and performance on standardized Math exams.
I spent some time this morning putting together 2005 data for New York State. New York has 698 school districts, but the plot below includes data only for 628 because of data issues (not reporting of districts, or no students taking a math regents … is that even possible?). The data come from 2005 because all of the data is not available yet for more recent years, and even then, I am not any good at extracting Access data (older data is in Excel). The chart below plots on the X-axis (the horizontal one) a measure of the poverty level in the school district (the New York State Education Department calculates an index for every district) and on the Y-axis plots the percentage of students passing a Math regents exam in the 10th grade.
The yellow line indicates a simple regression line through the data points. It says that school districts that have less poverty have a higher share of students passing the Math regents. This is completely unsurprising (the equation is in the box). Schools that are represented in dots above the line are those that have a higher share of students passing the regents than would be predicted by the level of poverty in their district (again, I warn that this is a simple regression controlling for nothing else), and those represented by dots below the regression line are those that have a smaller share of students pass the Math Regents than would be predicted by their level of poverty.
In summary, those districts above the line are over-performing while those below are under-performing. But the interesting question Arnold poses is how do expenditures per student compare for those districts that are over-performing versus those that are underperforming? Is the better performance because those schools have more money? You judge for yourself:
- Districts above the line spent, on average in 2005, $14,047 per student;
- Districts below the line spent, on average in 2005, $13,979 per student;
The over-performers outspent the under-performers by about the cost of a social studies textbook.
Michael,
The data appear to be highly nonlinear. I suggest you use decile groupings to rescale the data. That is, a school district gets a 10 if it’s in the top decile for pass rate, 9, if it’s in the next decile, etc. Do the same with the inverse poverty index. Then run the regression and see what happens.
One thing to keep in mind are cost of living differences, which are substantial between, say, Manhattan and Cooperstown. Manhattan schools have to pay teachers far more than small town schools.
You can get cost of living estimates for all small cities on up from ACCRA.
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