In this post I present some charts relating education outcomes to per-student funding for public schools at the state level.

The outcome measures I use are statewide average scores on various tests taken by students as part of the National Assessment of Educational Progress (NAEP). NAEP is a program of the U.S. Department of Education’s National Center for Education Statistics and is intended to measure “what America’s students know and can do in various subject areas.” Tests are given to representative samples of students from each state, allowing valid comparisons across states. Participation in the 4^th grade and 8^th grade assessments in reading and math is required for states to receive federal Title 1 funding. State participation in assessments of other subject areas is voluntary. (Much more on NAEP is available here; state comparison data are available here.)

The funding measures I use are from the Census Bureau’s annual Public Education Finances Reports, which document state average revenue per student from federal, state and local sources. (These reports are available here.)

On the first chart below, I have plotted average state scores in the reading test given to 8^th graders in January–March 2009 (vertical axis) against total funding per student in 2009 dollars averaged over he eight school years 2001–02 to 2008–09 (horizontal axis). The solid blue diamond is the data point for Washington. The plot shows a loose positive correlation between test scores and per student spending. (The correlation coefficient is 0.381.)

The straight line on the chart is the graph of a simple linear least-squares regression with the NAEP score as dependent variable and the eight-year average total revenue per student (in thousands of dollars) as the independent variable. The fitted equation is:

Standard errors for the coefficient estimates are shown in parentheses. The 0.95 value of the estimated coefficient for total funding  (F_T) suggests that a $1,000 per year increase in per student funding leads to a 0.95 point increase in the average 8^th grade reading NAEP score. The usual caution that correlation does not prove causality applies, of course.

By the standard t-test, the funding coefficient is significant at the 1 percent level. The adjusted R squared (0.1273) is not bad for a cross-sectional regression; spending, however, “explains” only a small fraction of the variation in among states. Washington students performed 4 points higher than would be predicted based on funding.

The second chart is more surprising, at least to me. On this chart, I have plotted average state 8^th grade reading scores on the 2009 NAEP against the share of funding coming from local sources. The plot shows a loose positive correlation between scores and the local funding share. The solid blue diamond is Washington.

Again, the line on this chart is the graph of a simple least-squares regression, the equation of which is:

The 17.3 value of the estimated coefficient for the local funding share (S_L) suggests that an increase of 0.1 in the local funding share (e.g. from 50 percent of total funding to 60 percent) leads to a 1.73 point increase in the average 8^th grade reading NAEP score. By the standard t-test, the local funding coefficient is significant at the 1 percent level. The adjusted R squared (0.1236) is only slightly smaller than that in the regression where total funding per student is the independent variable. The source of the funds “explains” almost as much of the variation in reading scores as the amount of funds!

Washington students performed 5 points higher than would be predicted based on funding.

A multiple regression with the 8^th grade reading score as the dependent variable and both per student funding and the local share as independent variables returns this equation:

The coefficients on funding and local share are both a bit smaller than in the corresponding simple regressions. Both coefficients are statistically significant at the 5 percent level. (And both miss being significant at the 1 percent level by only a small amount.)

Finally, here is the result of a multiple regression where the three independent variables are eight-year averages of per student federal funding (F_F), per student state funding (F_S) and per student local funding (F_L).

While the coefficient for federal funding is large and negative, the large standard error implies that the coefficient is not statistically different for zero at the 10 percent level. The coefficient for state funding is likewise not statistically different from zero at the 10 percent level. The coefficient for local funding is nearly three times larger than that for state funding and is significant at the 1 percent level.

I have repeated this analysis for 14 other NAEP exams: for 2005, 4^th grade reading, 4^th grade math, 8^th grade reading and 8^th grade math; for 2007, 4^th grade reading, 4^th grade math, 8^th grade reading, 8^th grade math and 8^th grade writing; and for 2009, 4^th grade reading, 4^th grade math, 4^th grade science, 8^th grade math and 8^th grade science. Click here to download the regression results and charts.

In all 14 cases there are both a positive correlation between average NAEP score and per student funding amount and a positive correlation between average NAEP score and share of funding from local sources. In all cases Washington students score higher than would be expected based on either per student funding amounts or the share of funds coming from local sources.