Exact Small-sample Rank Inference

How to use Exact Small-sample Rank Inference

Double average ranks to retain ties as integers. Dynamic programming counts every fixed-size label allocation for Mann–Whitney or every sign allocation after removing paired zero differences. The displayed two-sided probability is twice the smaller inclusive tail, capped at one.

1. Enter model json (schema and units below).
2. Choose the stated convention and check the units and supported model.
3. Calculate, inspect the result, then copy or download it.

Good to know

• Plain decimal JSON numbers or strings, at most six fractional places, magnitude at most 1,000,000,000; raw numeric spellings and duplicate object members are checked. Exact rational arithmetic is capped at 8,192 bits. Text is at most 30,000 characters; a local JSON download preserves exact fractions or full stored approximate numbers. Mann–Whitney: 1–15 observations per group. Signed rank: 1–24 equal-length pairs. These are exact conditional randomization distributions under exchangeability or sign symmetry, not proof that distributions or medians alone agree; no continuity correction or asymptotic fallback.
• Local calculation only; no input persistence or external lookup. Text/JSON is limited to 30000 characters and output to 1000000 characters. Numeric model inputs and precision/work limits are stated on this page. Approximate JSON numbers retain full stored values; exact arithmetic outputs retain decimal or fraction strings. Unsupported states fail explicitly.