The Observation Theory EncyclopediaFrom TSKAboutBy kindBy chapterBy Lean fileLedgerProvenance

family-wise error rate concept

DefinitionThe probability of at least one false alarm across a set of tests, at most the number of tests times the per-test threshold by the union bound. Primer S, equation S.16. Also family-wise, familywise.
ExampleForty tests at 0.05 have family-wise error rate 1 minus 0.95 to the fortieth, about 0.87.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id family-wise-error-rate, kind concept.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equation

Book equation S.16.

Assumptions and scopenone
Prior artnone recorded
Evidencenone
Reviewedsemantic review 2026-09-09; generated 2026-09-10 from records at the commits on the provenance page.

Equation

Book equation S.16.

\[\Pr[\text{at least one false alarm}]\le m\,\alpha,\qquad \alpha_{\mathrm{Bonf}}=\frac{\alpha}{m}.\]

Conditions

none

Ledger

none

First stated

Primer S section S.8 of Data Mining as Observation, added in draft 0.3 (2026-09-09) for the ECE 514 readers whose first courses are far behind. The idea is standard and TSK Appendix C covers it at length.

Measurements

none

Failures and corrections

none

Invariance envelope

none declared

Machine checked

none

Used in

Data Mining as Observation primer S, chapters 8.

Related

Bonferroni correction; multiple comparisons; p-value.

See also

none

Status

Generated 2026-09-10 by encyclopedia/generate.py; book at observation-data-mining f3914f0; the commit of every record is listed in the encyclopedia’s provenance.

← false positive ratefine-tuning →