Yup, educational statistics done here.
Your question is very tough to get your arms around. The “proof” is difficult to see.
We could go backwards…
If we cut ed spending would we expect test scores to go down? probably. This would show a positive correlation, but it doesn’t necessarily extrapolate to “increased” spending.
To look at this question “scientifically”, we need to define lots of terms. Different systems define “per pupil spending” differently. Some systems include such things as replacing library books in their pps numbers while other systems don’t.
Test scores are also difficult to pin down. We could look at, say, CTBS test scores over time and see a change, but we likely would not see the same changes in different test scores (SAT, or such).
We won’t even get into the problems of translating test scores to “knowledge absorbed” (vs. memorized for testing).
The biggest problem with addressing your question (and why you might not find DOE type info is that different systems and even schools spend pps money differently. One school might use a lot of it this year to purchase new text books while another might use the money to resource teachers. In this age of “Site Based Management”, individual schools have a lot of freedom in disbursment of money. While this may be good for schools, it does make answering your question difficult.
We (my office and I) have done quite a bit of work with “Value Added Assessment”, i.e., determing what proportion of score change is attributable to the schools (what value the schools add to the score). We have found (as have others) that schools account for 3-10% of variance in student outcomes, the rest being related to student factors out of the control of the school.
One of the better areas for increased funding for schools is the teacher staff. Having a qualified, experienced teaching staff has more of a correlation on student outcome scores than the number of chemicals in the chem lab or the number of microscopes int the biology classrooms.
For articles, I suggest you do an ERIC search or other journal search. Try the American Education Research Journal and such.