Why "Poverty" Outpredicts Income in Our Proficiency Models

Short answer
Both statements can be true at once:
- Income and poverty are strongly related.
- Poverty can still be the better predictor of proficiency.

Plain-language explanation
1) Income and poverty overlap, but they are not the same signal.
- In our school-level data, per-capita income and Students Experiencing Poverty are strongly related, but far from identical.
- Across ELA, Math, and Science, the scored-student-weighted correlation is about -0.65 to -0.66 for per-capita income and -0.60 to -0.62 for median household income.
- Even a correlation of -0.66 implies shared variance of about 44%, leaving substantial non-overlap.

2) The two measures are not equally close to the students being tested.
- Students Experiencing Poverty is a school-population hardship/composition measure.
- ACS per-capita income is a tract-level mean for all residents around a school.
- A measure tied to enrolled students usually tracks school outcomes more directly.

3) Per-capita income is a mean and can be skewed.
- High earners can raise tract mean income even when many enrolled students face hardship.
- That weakens income as a direct proxy for school hardship burden.

4) Poverty captures hardship channels more directly linked to learning disruption.
- ODE's poverty field reflects student hardship categories (for example SNAP/TANF eligibility, foster care, houselessness, migrant status).
- Those conditions can affect attendance continuity, stress load, and day-to-day school access.

5) The model results match this interpretation.
- In ordinary-school five-fold cross-validation tests, all outcomes and weights use students with reported Level 1-4 results:
- ELA:
- BA+ + Attendance + Median Household Income: 0.5152
- BA+ + Attendance + Poverty: 0.6516
- BA+ + Attendance + Median Household Income + Poverty: 0.6622
- Math:
- BA+ + Attendance + Median Household Income: 0.6394
- BA+ + Attendance + Poverty: 0.6750
- BA+ + Attendance + Median Household Income + Poverty: 0.6762
- Science:
- BA+ + Attendance + Median Household Income: 0.3803
- BA+ + Attendance + Poverty: 0.5072
- BA+ + Attendance + Median Household Income + Poverty: 0.5188

Interpretation
- Income remains useful as broad community context.
- Poverty appears to carry more independent school-level signal for proficiency.
- Concise framing:
"Income and poverty both matter, but poverty is a closer measure of student hardship and therefore a stronger predictor in this model framework."
- Plain-language formulation:
"Per-capita income is a neighborhood-wide average for everyone living in the school's tract, while the poverty measure reflects hardship among students actually enrolled in the school."

Caution
- These are school-level observational associations, not causal proof.