In a Parapundit comment thread discussing the fallacious debating ploys regularly employed by leftists and neocons, an illustrative commenter claims that smaller class sizes have been shown to be correlate strongly with better test scores. He references a study out of Tennessee. If the benefits of a smaller class size are so overwhelming, you'd assume they'd show up to some degree at the state level. But they do not. A relationship seemed unlikely since it wouldn't account for race. But even when race is taken into account, by looking at the difference between predicted and actual scores, student-to-teacher ratio and performance do not correlate at anything even approaching statistical significance (the p-value is .42). Nor do increased student expenditures or teacher salaries.
That race matters in the aggregate is a recurring theme here. State-level NAEP results evince this. Simply knowing the racial composition of a state 'explains' 72% of that state's performance. By contrast, per-pupil expenditures, teacher salaries (both adjusted for cost-of-living; without doing so, the relationship is even more feeble), and average classroom size combined explain a mere 15% of how a state fares, and even that figure is just outside 95% confidence (with a p-value of .06).
The conventional nostrums are impotent. More intelligent kids are the key to better NAEP performance, but IQ isn't something that can be sustainably juiced up in the classroom. There have been a plethora of attempts, but they are consistently met with failure. Ending unfettered Hispanic immigration in favor of a merit immigration system, encouraging health basics (breast-feeding, vitamin supplements), and revising tax policies that currently incentivize dysgenic birthing patterns (EITC, child tax credit, dependency phaseouts) will do orders of magnitude more than the educational reforms that've been reliably failing for half a century now.