Sets & relationships / Venn diagram
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Each circle (or ellipse) is a set; the number in a region counts items that belong to exactly those sets and no others (exclusive counts). Set sizes are shown in brackets.
The region table lists the items in every region for further analysis; the membership matrix shows which sets each item belongs to.
The Jaccard index (intersection / union) and the overlap coefficient (intersection / size of the smaller set) compare sets of different sizes.
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. Shapes cannot be area-proportional for 4 or more sets; use an UpSet plot for many sets.
Pairwise overlap test: upper-tail hypergeometric probability P(X ≥ k) with X ~ Hypergeom(N, |A|, |B|) (equivalent to a one-sided Fisher exact test), BH-adjusted (Benjamini & Hochberg 1995). Four to six sets use a fixed symmetric ellipse layout.
2–6 sets, up to 200,000 items per set.
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