Sign-flip Simpson: homework and test scores

Question

Across all students in a K-12 school, plotting weekly homework hours against test scores gives a downward slope: students who do more homework score lower. Yet within each grade level, the slope is upward: more homework goes with higher scores.

Reconcile the negative school-wide slope with the positive within-grade slopes. Which relationship reflects the causal effect of homework on a student?

Accepted Answer

This is Simpson's paradox in continuous form. The confounder is grade level. What is happening. Older grades are assigned much more homework and sit harder exams that produce lower raw scores; younger grades get little homework and take easier tests with higher scores. Across the whole school, then, "more homework" travels with "older grade," and older grades have lower raw scores, so the pooled slope is negative, driven by grade level, not by homework. Within a single grade, where the workload norms and test difficulty are fixed, the students who do more homework score higher: a positive slo…

Sign-flip Simpson: homework and test scores

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