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SELECTED STUDIES · METHODS · AL-198 · #184
Levels-of-Analysis Lab
The Reversal Detector (AL-186) catches Simpson's paradox across strata of the same table. This tool catches the other classic mix-up: a correlation computed across group means (ecological, aggregate level) can point a different direction, or a wildly different magnitude, than the correlation among the individuals inside those groups (Robinson 1950). Paste a group-level table of means, and enter the known or assumed individual-level correlation, to see whether the aggregate story would mislead you.
Method: n-weighted Pearson correlation across group means (closed-form arithmetic), compared against a user-supplied individual-level r. Robinson example reproduces published 1950 textbook figures (informational, not raw microdata). School-income example is a synthetic illustration, not real school data. data_vintage: static, never refreshed.
Robinson (1950), the textbook reversal, for reference
Robinson's original example used 1930 U.S. Census data on % foreign-born and % illiterate. Across states, the correlation was positive, roughly +0.53 (states with more foreign-born residents tended to show higher illiteracy). Among individuals, the correlation was negative, roughly −0.11 (a foreign-born person was, if anything, slightly less likely to be illiterate than a native-born person, since foreign-born immigrants settled disproportionately in higher-illiteracy states for reasons unrelated to their own literacy). The sign flips entirely between levels. These are the published textbook figures, shown for reference only; use the group table below to run the same comparison on your own data.
Setup
Group-Level Means Table
Group Means Entered
Ecological (Group-Level) vs Individual-Level Correlation