confidence interval concept
| Definition | A range that would contain the true value in a stated fraction of repeated samples, usually 95 percent. Chapter 0 section 0.9. Also inside the interval, with interval. |
|---|---|
| Example | A mean of 0.62 with standard error 0.04 has a 95 percent interval of about 0.54 to 0.70. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id confidence-interval, 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/ConfidenceInterval.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- A range that would contain the true value in a stated fraction of repeated samples. An interval with coverage one minus alpha misses in a fraction alpha, over m independent intervals the expected misses are m alpha and the chance that all cover is one minus alpha to the m, and the chance that at least one misses is at most m alpha.
- Nine intervals at ninety-five percent have a chance near seven percent of two or more misses, which is how the re-gate table’s seven of nine inside the interval is read.
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 intervals in the re-gate table of chapter 14 and the hubness intervals of chapter 11.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/ConfidenceInterval.lean,
theorems missRate_eq, some_miss_le,
nine_intervals, nine_expected, 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, 6, 8, 14.
Related
bootstrap; standard error; p-value; preregistration.
See also
Book equations stated beside the entry’s terms, not defining it: 8.3, 8.2.
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.