Sets & relationships / Proportional Venn (Euler)
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Circle areas are proportional to set sizes, and overlap areas approximate intersection sizes, so differences in size and overlap are visible at a glance.
With three sets, centre distances are solved from each pairwise intersection and the circles are then placed by triangulation, so the three-way region is generally not exact; rely on the numbers printed in each region (exclusive counts).
The region table lists the items in every region; the pairwise table gives the Jaccard index and the overlap coefficient.
With a background size N (for example all genes detected), each pairwise overlap is tested against random expectation with the hypergeometric distribution, with BH adjustment.
The area-proportional layout is an Euler-diagram approximation (circle area ∝ set size, centre distances solved numerically from pairwise intersection areas, three circles placed by triangulation); pairwise overlaps are tested with the upper-tail hypergeometric probability P(X ≥ k) (equivalent to a one-sided Fisher exact test), BH-adjusted (Benjamini & Hochberg 1995).
2–3 sets, up to 200,000 items per set.
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