Spending and Class Size vs Performance: Findings Memo

Spending and Class Size vs Performance: Findings Memo
Regenerated: 2026-08-06

Scope
- Data: 2024-2025 processed English, Math, Science school rows.
- Outcome: Percent Proficient, reconstructed as Number Proficient / Scored Performance Denominator.
- Predictors of interest: Overall spending per student, Classroom spending per student, Median class size.
- Context controls (baseline continuity spec): Per-capita income, Adult BA+ rate, Regular attendance.
- Companion context spec: Students Experiencing Poverty, with censored AAG disclosures represented by documented interval midpoints and their raw tokens/bounds preserved upstream.
- Weighting: students with reported Level 1-4 results.

Methods used
1) Weighted bivariate checks (correlation and simple slope).
2) Weighted multivariable OLS-style checks with controls.
3) Weighted ridge regression with 5-fold CV (to stabilize collinear spending variables).
4) District fixed-effects ridge (within-district demeaning) with CV and permutation importance.

Executive summary
- Your chart-level impression is largely confirmed:
  class size shows little robust predictive contribution once SES and attendance are included.
- Spending shows a detectable but inconsistent contribution and is highly sensitive to context specification and model frame.
- Education and attendance remain dominant in pooled models and many fixed-effects models, but not every poverty-controlled fixed-effects result.
- Income is generally intermediate: weaker than education and attendance, often similar to or above spending.
- The poverty-aware fixed-effects sensitivity is a qualification: the combined spending signal is notably larger for Math and Science than in the pooled poverty models, so a single project-wide rank ordering is too strong.

Key findings by factor
1) Median class size
- Bivariate association can appear positive.
- After controls and regularization, standardized effects are near zero in all subjects.
- Permutation importance is near zero in most settings.
- Interpretation: class size is not a strong standalone predictor in these school-level cross-sections.

2) Spending (overall/classroom)
- The two spending variables are highly collinear (weighted corr ~0.85 to 0.88).
- Ridge regularization was necessary to reduce coefficient instability.
- Combined spending signal (permutation drop in CV R2):
  - Per-capita-income spec, non-FE ridge: English 0.065, Math 0.013, Science 0.090.
  - Per-capita-income spec, FE ridge: English 0.307, Math 0.018, Science 0.061.
  - Poverty spec, non-FE ridge: English 0.010, Math 0.011, Science 0.010.
  - Poverty spec, FE ridge: English 0.001, Math 0.153, Science 0.093.
- Interpretation: spending can carry a secondary signal, but strength is uneven across subjects, context controls, and model frames.
  The English income-spec FE result and the Math/Science poverty-spec FE results should be treated as sensitivity findings, not stable effects, until replicated with lagged spending and alternative fixed-effects specifications.

3) Education, attendance, income
- Education and attendance produce the largest predictive contribution in the pooled models and most income-spec fixed-effects results.
- Math FE ridge particularly emphasizes attendance.
- Income remains meaningful but below education/attendance in most configurations.
- Under the poverty-spec fixed-effects lens, combined spending exceeds BA+ in Math and exceeds both BA+ and attendance in Science; this exception is why the findings are described as model-sensitive rather than placed in a single ordering.

How to interpret the apparent contradictions
- Sign flips and coefficient changes across models are expected under strong collinearity
  (especially between overall and classroom spending).
- Permutation importance is more stable for relative contribution than raw coefficient signs.
- FE models answer a different question (within-district differences) than pooled models
  (between + within combined), so effect sizes are not directly interchangeable.

What this means for the project
- It is reasonable to say:
  "At this stage, class size remains weak, while spending is model-sensitive: usually secondary in pooled statewide models but more prominent in several fixed-effects specifications."
- It is not yet reasonable to say:
  "Spending has no effect."
  This data structure (single-year spending, high collinearity, cross-sectional school aggregates) limits causal interpretation.

Recommended next analyses (highest value first)
1) Lag-aligned resource models
- Match outcomes to prior-year or multi-year averaged spending/class-size where possible.
- Rationale: test outcomes may respond to resource conditions with delay.

2) FE + regularized nonlinear checks
- Add spline terms for spending and attendance under ridge/elastic-net.
- Rationale: linear effects may understate threshold or diminishing-return structure.

3) Spending decomposition
- Replace or augment the available spending measures with more policy-proximal components
  (instructional share, staffing mix, support services, etc., if available).
- Rationale: total spending may mask the relevant channel.

4) Robustness by school level (elementary/middle/high)
- Run the same ridge/FE stack by school level.
- Rationale: resource-performance coupling may differ by grade span.

Files produced
- Technical model report:
  docs/spending_class_size_ridge_report.txt
- Companion OLS-style report:
  docs/spending_class_size_effects_report.txt
- Scripts:
  scripts/report_spending_classsize_ridge.py
  scripts/report_spending_classsize_effects.py