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About this tool
Compare per-group and aggregate correlations from grouped x/y data, then flag potential Simpson's-paradox reversals where the trends disagree.
The Correlation & Simpson's Paradox Visualizer computes the Pearson correlation coefficient r separately inside each group of your data and again on the pooled data, then flags Simpson's paradox — the case where every group's r points one way but the aggregate r points the other. You paste rows as "Group | x | y", set a minimum group size (default 2), and get each within-group r to six decimals alongside the aggregate. It is for anyone checking whether a headline correlation survives once the data is split by the variable that actually separates the observations.
Open Correlation & Simpson's Paradox Visualizer on AltFTool — it loads instantly in your browser.
Paste your data into 'Grouped x/y observations' as Group | x | y, one row per line, or load the 'Reversal example' preset.
Set 'Minimum observations per group' to 2 or higher so undersized groups are left out of the group table.
Read 'Possible Simpson's-paradox reversal' or 'No full sign reversal detected' above the aggregate r, with each group's n and within-group Pearson r listed below.
Each group's Pearson r and n are tabled against the aggregate, so a disagreement is visible instead of inferred.
It compares the sign of every qualifying group's r against the sign of the aggregate and says outright whether a full reversal is present.
Groups below your threshold are excluded from the group table, so a two-point group cannot manufacture a spurious sign.
It is when a correlation or trend present in every subgroup disappears or flips sign once the subgroups are combined. The classic cause is a lurking variable that determines both group membership and the outcome — the 1973 Berkeley admissions case is the standard example, where the pooled data suggested bias against women but department-by-department it did not.
It flags a reversal only when every group that meets your minimum size has a non-zero r of the same sign and the aggregate r has the opposite sign. A mix of positive and negative group correlations, or an aggregate r of exactly zero, reports as no full sign reversal.
Pearson's r, reported to six decimal places and bounded between -1 and +1. Pearson measures linear association only, so a strong curved relationship can still show an r near zero — plot the points before trusting any single coefficient.
Pearson's r is undefined for a single point, and the tool returns 0 for any group with fewer than two rows. The minimum is set to 2 by default and cannot go lower; raising it to 5 or 10 is usually wiser, because r from two or three points is dominated by noise. This is exploratory analysis, not a significance test — consult a statistician before drawing conclusions from it.
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