C.16:6 - Scale-type admissibility quick reference (Informative)
Didactic note. This table is a memory aid for engineers and managers. It does not introduce new admissibility rules. Normative admissibility of operations by scale type is governed by A.18 (CSLC) and, where mechanized in CG‑frames, by the relevant admissibility profiles. If any row below conflicts with A.18, treat it as an illustrative example and follow A.18.
| Scale type | Comparisons | Location | Differences | Ratios | Admissible summaries | Typical unsupported anti-patterns |
|---|---|---|---|---|---|---|
| Nominal | =, ≠ | mode, frequencies | — | — | counts, proportions | averaging labels; ordering categories without a declared order |
| Ordinal | <, =, > (rank) | median, quantiles | not meaningful | — | order‑respecting summaries (median rank, percentiles) | arithmetic mean of ranks; variance on ranks; linear blends of ranks |
| Interval | <, =, > | mean location | Δ meaningful | ratio not meaningful | mean, sd of differences, correlation | ratio claims (“twice as hot” in °C); geometric mean |
| Ratio | <, =, > | mean location | Δ meaningful | ratios meaningful | arithmetic/geometric means, cv, growth rates | adding heterogeneous units; log on nonpositive values |
Reminders (informative; see A.18 for normative rules). G‑1 (Order). On ordinal, transforms should be monotone. G‑2 (Differences). On interval or ratio, Δ is meaningful; on ordinal or nominal, it is undefined. G‑3 (Ratios). Only ratio Scales admit x/y semantics; interval, ordinal, or nominal do not. G‑4 (Unit coherence). Interval or ratio arithmetic presumes compatible units (or a declared conversion). G‑5 (Target polarity). If polarity is targeted, comparisons use distance‑from‑target semantics as declared by the relevant subject pattern, template, and cited method or mechanism.
(These rules line up with the MM‑CHR exposition of CSLC and term discipline; A.17 fixes the lexical side.)