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p-value concept

DefinitionThe probability of seeing a difference at least as large as the one observed if the true difference were zero. Chapter 0 section 0.9. Also at p .
ExampleA score more extreme than 970 of 1000 null scores has p-value 0.03.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id p-value, kind concept.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equationnone
Assumptions and scope
  • Against a finite null sample, the fraction of null draws at least as large as the observation. It lies in the unit interval, never rises as the observation grows, and under the null the fraction of draws with p-value at or below a level is at most that level, which is what makes a threshold on it a false-positive rate.
  • A p-value counts one look. Forty looks at five percent pass two by chance, and the book’s rule is to count every comparison made and correct for it.
Prior artnone recorded
Evidencelean/DataMiningAsObservation/PValue.lean
Reviewednot yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.
countrowsthreshold
The fraction of the null distribution at least as extreme as the observation.

Equation

none

Conditions

Conditions are curated in entries.toml rather than read from a record.

Ledger

none

First stated

Chapter 0 section 0.9 of Data Mining as Observation, with the program’s own p-values in the ensemble comparison of chapter 7 and the C-12 record in readscope.

Measurements

none

Failures and corrections

none

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/PValue.lean, theorems pvalue_mem_unit, pvalue_antitone, uniform_bound, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

Used in

Data Mining as Observation primer S, chapters 0, 11.

Related

multiple comparisons; confidence interval; harness; preregistration.

See also

Book equations stated beside the entry’s terms, not defining it: 8.3.

Sources-table rows that share a record with the entry without naming it: chapter 6 section 6.4, chapter 8 section 8.5.

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.

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