Simpson Paradox and Group Rate Checker
See how different task difficulty mixes can reverse an overall result even when a second strategy performs better in each category. Enter successful attempts and total attempts—not just percentages—for every group.
Why the default example flips
Within easy exercises, B has 19 successes out of 20 attempts (95%) and A has 81 out of 90 (90%). Within hard exercises, B has 16 out of 80 (20%) and A has 1 out of 10 (10%). B has a higher rate in both task categories. Yet overall, B has 35 successes in 100 attempts (35%), while A has 82 of 100 (82%). The task mix is different: 90% of A's cases are easy versus 20% of B's cases. Pooling without considering task difficulty therefore reverses the descriptive comparison.
This is an original synthetic teaching dataset, not an experimental benchmark or real student outcome. The Correlation, Confounding and Simpson's Paradox Guide explains why no arithmetic reversal by itself tells us that a strategy caused anything. The Pearson Correlation Calculator handles a different problem: a numerical relationship across paired observations.
Source and research limits
Stanford Encyclopedia of Philosophy: Simpson's Paradox discusses how subgroup and pooled associations can disagree, and the role of causal reasoning. Penn State's regression methods also explain how omitting relevant variables can reverse associations. These resources do not authorize treating the highest subgroup rate as an automatic causal estimate. In real studies, the correct grouping and whether to adjust for another variable depend on the research question and the data-generating process.