BA+ Association Across School-Poverty Bands Corrected purpose-sensitive rebuild: 2026-09-10. Original artifact date retained in filename: 2026-02-21. Question Within ordinary neighborhood elementary schools, how does the descriptive association between school-address tract adult BA+ and official All Grades proficiency vary across enrolled-student poverty bands? Primary estimand and units - Academic year: 2024-2025; Total Population official ODE All Grades rows only. - Primary universe: explicit ODE Regular schools, excluding charter, virtual, and curated special-enrollment flags, with a nonempty cross-subject observed tested-grade set confined to grades 3-5. - Middle schools (tested grades confined to 6-8) are a labeled sensitivity; mixed-grade and high-school profiles are excluded. - Proficiency is percentage points from exact Level 3 + Level 4 counts divided by the equal Scored Performance Denominator identity. Weights are scored students. - BA+ is school-address tract adult percentage points; SEP is enrolled-student percentage points; attendance is tested-grade regular-attender percentage points. - Primary SEP uses exact values plus the ETL's documented interval midpoint for valid left-censored values (2.5 points for <5%). Midpoints are estimates, not exact observations. - Lower/upper endpoints and an exact-only complete-case analysis are separately labeled sensitivities. - All R^2 values below and in the companion table are explicitly in-sample descriptive fit. This band analysis does not conduct a formal slope-heterogeneity test. Primary elementary documented-midpoint SEP results - ELA: overall BA+ slope +6.65 proficiency points per +10 BA+ points; low-poverty descriptive slope +4.56; high-poverty descriptive slope +2.56; within high poverty, adjusted BA+ slope +1.69 and added in-sample weighted R^2 0.037 (235 schools; 42,534 scored students). - Math: overall BA+ slope +6.66 proficiency points per +10 BA+ points; low-poverty descriptive slope +6.04; high-poverty descriptive slope +2.18; within high poverty, adjusted BA+ slope +1.48 and added in-sample weighted R^2 0.030 (234 schools; 42,261 scored students). - Science: overall BA+ slope +5.87 proficiency points per +10 BA+ points; low-poverty descriptive slope +4.98; high-poverty descriptive slope +2.39; within high poverty, adjusted BA+ slope +1.67 and added in-sample weighted R^2 0.045 (215 schools; 13,825 scored students). - Sensitivity conclusion: BA+ slopes remain positive in every elementary poverty band under lower-endpoint, midpoint, upper-endpoint, and exact-only SEP treatments; endpoint choice does not reverse the descriptive direction. Coverage - ELA elementary (primary): 457 validated BA/attendance rows before SEP-scenario missingness; 13 rows omitted for unavailable or invalid attendance. - ELA middle (sensitivity): 188 validated BA/attendance rows before SEP-scenario missingness; 5 rows omitted for unavailable or invalid attendance. - Math elementary (primary): 456 validated BA/attendance rows before SEP-scenario missingness; 13 rows omitted for unavailable or invalid attendance. - Math middle (sensitivity): 187 validated BA/attendance rows before SEP-scenario missingness; 5 rows omitted for unavailable or invalid attendance. - Science elementary (primary): 433 validated BA/attendance rows before SEP-scenario missingness; 5 rows omitted for unavailable or invalid attendance. - Science middle (sensitivity): 188 validated BA/attendance rows before SEP-scenario missingness; 2 rows omitted for unavailable or invalid attendance. Interpretation - BA+ remains a school-site tract context measure, not a student-family measure or an attendance-area average. The elementary primary universe is therefore substantively important. - Differences between poverty-band slopes are descriptive. No formal slope-heterogeneity inference is supported or supplied here. - Adjusted band fits are in-sample associations controlling for continuous SEP and attendance within the band. They are not out-of-sample validation and are not causal effects. - Numeric statements above are derived directly from the machine-readable companion table. Machine-readable companion - ba_signal_in_high_poverty_summary_2026-09-10.csv: scope, SEP scenario, band limits, units, coverage, slopes, correlations, and explicitly in-sample R^2 fields.