VennScope Learn · v0.16

Understand the analysis, not just the picture.

A compact course for researchers, students, analysts and anyone who wants to understand sets, Venn diagrams, UpSet plots, similarity measures, overlap statistics and biological identifiers before interpreting a figure.

What this course covers

These lessons explain established mathematical, statistical and biological concepts used in set analysis. They do not disclose VennScope's proprietary source code, internal implementation architecture, optimisation choices or deployment details.

Module 01 · Foundations

Sets, unions and intersections

A set is a collection of distinct elements. In VennScope an element can be a gene symbol, accession number, sample identifier, category, keyword or any other value that can be compared for membership.

Notation	Meaning
A ∪ B	Union: elements in A, B or both.
A ∩ B	Intersection: elements present in both A and B.
\|A\|	Cardinality: number of distinct elements in A.
A \ B	Elements in A that are not in B.

Worked example. If A = {A, B, C, D} and B = {C, D, E}, then |A| = 4, |B| = 3, A ∩ B = {C, D}, and A ∪ B = {A, B, C, D, E}.

Module 02 · Venn diagrams

What a Venn diagram shows

Venn diagrams use overlapping closed shapes to represent relationships among sets. John Venn developed the diagrammatic system in the nineteenth century; modern use extends from logic and mathematics to education, biology and general data analysis.

For two or three sets, Venn diagrams are intuitive because every possible membership region can be shown clearly. With many sets, the number of possible intersections increases rapidly and circle-based layouts become difficult to read.

Exact versus inclusive intersections

Exact A ∩ B means elements that belong to A and B and to no other displayed set. Inclusive A ∩ B means elements shared by A and B regardless of whether they also occur in additional sets.

For three sets A, B and C, an element in all three belongs to the inclusive A ∩ B overlap, but it does not belong to the exact A ∩ B-only region.

Try it: load the 3-set synthetic example and switch between Exact and Inclusive.Open 3-set example

Module 03 · Multi-set comparison

Why UpSet is useful

UpSet plots represent intersections using a matrix of set-membership combinations and bars for intersection sizes. They are usually easier to interpret than a many-circle Venn diagram once the number of sets grows beyond three or four.

The important scientific quantities are the membership combinations and their counts. The visual geometry is a representation of those values; it should not be mistaken for a spatial measurement.

Try it: VennScope's 8-set example switches to UpSet automatically.Open 8-set example

Module 04 · Similarity

Jaccard, Dice and overlap coefficient

Different similarity coefficients answer slightly different questions. No single coefficient is universally best.

Jaccard(A,B) = |A ∩ B| / |A ∪ B| Dice(A,B) = 2|A ∩ B| / (|A| + |B|) Overlap coefficient(A,B) = |A ∩ B| / min(|A|, |B|)

Jaccard penalises non-shared elements through the union. Dice gives shared elements twice the weight in the numerator. The overlap coefficient reaches 1 when the smaller set is completely contained in the larger set.

Interpretation matters. A high overlap coefficient can coexist with a lower Jaccard value when one set is much smaller and mostly contained within another.

Module 05 · Statistical overlap

Why a background universe is required

A p-value for overlap asks whether the observed overlap is unusual relative to a defined population of possible elements. Without a background universe, that probability model is incomplete.

For gene lists, the appropriate universe is often the set of genes that could realistically have been observed in the experiment, not automatically every known gene in a database.

Hypergeometric enrichment

The hypergeometric distribution describes sampling without replacement from a finite population. For set overlap, an upper-tail probability can quantify how surprising it is to observe at least the measured overlap under a random-membership model.

P(X ≥ k) = Σ [ C(K,x) C(N−K,n−x) / C(N,n) ]

Here N is the universe size, K is the size of one set in the universe, n is the size of the other set, and k is the observed overlap.

Fisher's exact test

Fisher's exact test evaluates association in a 2×2 contingency table while conditioning on the margins. VennScope reports a two-sided Fisher p-value alongside the one-sided hypergeometric enrichment probability.

Odds ratio and confidence interval

An odds ratio above 1 indicates enrichment of co-membership relative to the chosen universe; below 1 indicates depletion. Confidence intervals express uncertainty in that estimate.

Try it: use a synthetic 3-set analysis and open the Statistics view. Supply a scientifically appropriate universe.Open statistics tutorial

Module 06 · Multiple testing

p-values, q-values and Benjamini–Hochberg

A p-value is not the probability that a hypothesis is true. It is a probability calculated under a specified null model. When many hypotheses are tested, the chance of obtaining small p-values by chance increases.

The Benjamini–Hochberg procedure controls the expected false discovery rate (FDR) under its assumptions. VennScope reports BH-adjusted q-values across the displayed family of pairwise Fisher tests.

q(i) = min over j≥i of [ m × p(j) / j ], bounded at 1

Statistical significance is not the same as biological importance, effect size or reproducibility. Interpret the p/q-value together with set sizes, odds ratio, study design and domain knowledge.

Module 07 · Why a t-test is different

Membership data are not continuous replicate measurements

A t-test compares numerical measurements between groups under a model of means and variability. A plain list of identifiers only says whether an element is present in a set; it does not provide replicate measurements or quantitative abundance values.

Therefore VennScope does not apply a t-test to ordinary set lists. A future quantitative-analysis module can support appropriate tests after users provide an abundance matrix and sample metadata.

Module 08 · Biological identifiers

Gene, transcript and protein IDs are related — but not interchangeable

Identifier	What it represents
Gene symbol	A human-readable gene name/symbol; for human genes HGNC maintains approved nomenclature.
HGNC ID	A stable identifier assigned by the HUGO Gene Nomenclature Committee for human genes.
NCBI Gene ID	A stable numeric identifier used by NCBI Gene.
Ensembl Gene ID	An Ensembl stable identifier for a gene feature.
Ensembl Transcript ID	An Ensembl stable identifier for a transcript; one gene can have multiple transcripts.
Ensembl Protein ID	An Ensembl stable identifier for a translated protein product.
UniProtKB accession	A stable accession used to identify a UniProtKB protein entry.
RefSeq accession	An NCBI accession for a curated/reference sequence record; nucleotide and protein accessions are distinct classes.
NCBI Taxonomy ID	A numeric identifier for an organism/taxon, such as 9606 for Homo sapiens.

Mappings can be one-to-one, one-to-many, many-to-one or unavailable. For example, collapsing protein identifiers to a gene level can merge several protein products. VennScope therefore treats mapping as an explicit workflow and preserves the original identifiers.

Learn the sources: see which public reference services VennScope uses and what provenance is recorded.Identifier sources

Module 09 · Tutorials

Practice with synthetic data

Tutorial 1

Your first 3-set Venn

Load three sets, inspect exact/inclusive regions, compare Elements and edit the figure.

Start tutorial

Tutorial 2

Eight sets with UpSet

See why UpSet is a clearer representation when intersection structure becomes complex.

Start tutorial

Tutorial 3

Overlap statistics

Define a universe and interpret Fisher, hypergeometric, odds-ratio and BH-adjusted results.

Start tutorial

Tutorial 4

Publication figure workflow

Edit typography and margins, review figure information and export a publication package.

Start tutorial

References & primary resources

Where to read further

UniProt — ID Mapping documentation ↗ Ensembl — REST API documentation ↗ HGNC — human gene nomenclature ↗ NCBI Gene ↗ NCBI RefSeq ↗ NCBI Taxonomy ↗

The Learn material is educational and is not a substitute for study-specific statistical or bioinformatics advice.