Statistical results overview Updated: 2026-07-16 Purpose - Provide one reader-facing, auditable summary of the main numeric findings produced by the Evidence Lab scripts. - Put effect sizes, ordering, and robustness checks in one place so interpretation is not spread across many files. Data scope and modeling setup - Unit of analysis: school-level aggregate rows (not student-level microdata). - Weighting: students with reported Level 1-4 results unless noted otherwise. - Main outcome for most analyses: Percent Proficient. - Baseline continuity predictors: adult BA+ rate, income, attendance. - Companion 2024-25 predictors: adult BA+ rate, Students Experiencing Poverty, attendance. - Exploratory predictors: overall spending per student, classroom spending per student, median class size. - Typical row filter: "Total Population" student-group rows, with "All Grades" rows dropped when grade-specific rows exist. How to read coefficients in this report - Correlation r: raw association only (no controls). - Standardized beta: relative predictor strength after controlling for other variables in the same model. - R^2: share of weighted variance explained by the model. - Delta R^2: improvement in fit after adding terms. 1) Joint SES + attendance models (core result) Supporting Evidence Lab material: SES + Attendance Joint Model Report and its source script. Results by subject (standardized betas from Percent Proficient ~ income + education + attendance): - English (ELA): income 0.024, education 0.464, attendance 0.298, R^2=0.417 - Math: income 0.045, education 0.433, attendance 0.412, R^2=0.517 - Science: income 0.005, education 0.459, attendance 0.252, R^2=0.349 What this means: - Education and attendance carry most of the controlled signal. - Income remains correlated in bivariate views, but in joint models its unique contribution is small in these statewide runs. - The education-over-income ordering is large and consistent across subjects. 1b) Poverty-aware reassessment (2024-25 companion result) Supporting Evidence Lab materials: Income and Poverty Reassessment Note, Why School Poverty Can Outpredict Income, and BA+ Signal in High-Poverty Schools. Cross-validated R^2 (ordinary schools): - ELA: - BA+ + Attendance + Income: 0.5152 - BA+ + Attendance + Poverty: 0.6516 - BA+ + Attendance + Income + Poverty: 0.6622 - Math: - BA+ + Attendance + Income: 0.6394 - BA+ + Attendance + Poverty: 0.6750 - BA+ + Attendance + Income + Poverty: 0.6762 - Science: - BA+ + Attendance + Income: 0.3803 - BA+ + Attendance + Poverty: 0.5072 - BA+ + Attendance + Income + Poverty: 0.5188 Interpretation: - In 2024-25 models, Students Experiencing Poverty adds meaningful independent signal. - Income still contributes context and modest incremental value in some subject/spec combinations. - Practical reading: keep income as community context, but include poverty-aware specifications for 2024-25 explanatory comparisons. - Note on comparability: these values use the median-household-income continuity spec; per-capita-income variants (reported in the poverty explainer note) show slightly different baseline R^2 values. 2) Interaction checks (non-additive structure) Supporting Evidence Lab material: Income, Education, and Attendance Interaction Report and its source script. Base model vs interaction model: - ELA: R^2 rises from 0.417 to 0.433 (Delta 0.015) - Math: R^2 rises from 0.517 to 0.547 (Delta 0.031) - Science: R^2 rises from 0.349 to 0.380 (Delta 0.031) The largest interaction term is usually education x attendance. Interpretation: - The association between one predictor and performance depends on the level of another predictor. - Purely additive narratives miss some structure in the data. 3) Stability and historical robustness Supporting Evidence Lab materials: split-stability source and report, plus the pre-pandemic 2018-19 model variants. Key findings: - Split-sample checks repeatedly preserve education > income ordering. - Pre-pandemic (2018-2019 Math, era-appropriate ACS) preserves the same ordering. - Magnitudes move with scope restrictions (for example, grade/school-level filters), but ordering remains stable. Interpretation: - The 2024-25 findings are unlikely to be a one-off artifact of one sample slice. 4) Outcome-level heterogeneity (Math, level-specific checks) Supporting Evidence Lab material: Income + Adult Education model source; Math Level 4 is the example below. Percent Level 4 example: - Weighted r: income 0.500, education 0.625 - Standardized betas: income 0.132, education 0.534 - R^2 (income + education): 0.399 Interpretation: - Education signal can strengthen for top-end outcomes, not just overall proficiency. 5) Spending and class-size exploratory models Supporting Evidence Lab material: Spending and Class Size vs Performance memo and companion source scripts. Observed pattern: - Class size: weak and often near-zero contribution after controls. - Spending: detectable in some specifications, but weaker and less stable than education/attendance. - Spending variables are strongly collinear, requiring regularization and cautious interpretation. Interpretation: - These school-level cross-sections do not support a strong, clean statewide class-size signal. - Spending likely has context-specific effects, but broad aggregate signal is modest in this setup. 6) Comparative signal strength Strongest recurring signals: - Adult education level - Attendance - School-population poverty (2024-25 ODE field) Secondary/variable signal: - Income after controls Weakest statewide signal in these cross-sectional models: - Median class size - Some spending specifications Cautions and limits - Associational evidence only; not causal identification. - School-level aggregation can hide within-school heterogeneity. - Collinearity can destabilize coefficient signs and magnitudes. - Best practice is to rely on ordering + stability + consistency across multiple model families. Replication materials The grouped Reports and Source Scripts index pairs the detailed reports with commented source scripts and downloadable text or machine-readable outputs.