p-value concept
| Definition | The 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 . |
|---|---|
| Example | A score more extreme than 970 of 1000 null scores has p-value 0.03. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id p-value, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/PValue.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- 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.
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.