attribute type concept
| Definition | The declaration of which transformations of a column keep its meaning, any injective relabelling for nominal, a strictly increasing map for ordinal, an affine map for interval, and a positive rescaling for ratio, nested in that order. Chapter 2 section 2.1. Also nominal, ordinal, interval scale, ratio scale. |
|---|---|
| Example | Temperature in Celsius is an interval scale, so a ratio of two temperatures means nothing, while 4 metres is twice 2 metres on the ratio scale of length. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id attribute-type, 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/AttributeType.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- The declaration of which transformations of a column do not change its meaning. A ratio scale permits a positive rescaling, an interval scale an affine map with positive slope, an ordinal scale a strictly increasing map, and a nominal scale any injective relabelling, and the four classes are nested in that order.
- A rescaling preserves ratios and an affine map preserves ratios of differences, so a consumer that reads a ratio of two interval-scale columns reads the origin the scale said was arbitrary.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Stevens, on the theory of scales of measurement, 1946, as chapter 2 section 2.1 of Data Mining as Observation reads it after TSK section 2.1.
Measurements
| Where the book states it | Numbers, as the book’s sources table records them | Source |
|---|---|---|
| chapter 2 section 2.1 | the four attribute types and permitted transformations | TSK 2e section 2.1 |
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/AttributeType.lean,
theorems scale_affine, affine_strictMono,
strictMono_injective, scale_preserves_ratio,
affine_preserves_difference_ratio, at
observation-data-mining f3914f0; what the check covers is stated in the
book’s appendix
C.
Used in
Data Mining as Observation chapters 2, 13.
Related
standardization; discretization; quotient.
See also
Book equations stated beside the entry’s terms, not defining it: 2.1, 0.12a.
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.