On the Theory of Scales of Measurement

Stevens, S. S. (1946). On the Theory of Scales of Measurement. Science, 103(2684), 677-680.

Type

Journal article

Intellectual base

Primary research

Year

1946

Volume

103

Issue

2684

Pages

677-680

DOI

10.1126/science.103.2684.677

DOI registrant

American Association for the Advancement of Science

Link

https://doi.org/10.1126/science.103.2684.677

Cited from

philosophy, statistics_experimental_design

Cited by

8 citations across 7 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Commensurability
  • Commensurability concerns whether different types of value can be compared, an orthogonal axis that Stevens (1946) makes explicit in his typology of measurement scales (nominal, ordinal, interval, ratio), where scale type and inter-scale comparability are independent properties.

    This sourceCanonical typology of measurement scales (nominal, ordinal, interval, ratio); supports the discreteness-vs-commensurability contrast by establishing that scale type is independent of whether two scales can be compared on a common metric.

• Continuum (measurement)
  • Its autonomous core is gradated state representation, distinct from topological continuity as a formal property, an uncountably infinite set generally, a mere spectrum metaphor or categories that only happen to be ordered.
  • This conserved decision sequence is the basis for Prime status.
• Measurement
  • A target attribute (the mapped property). A specific attribute of a target system — often implicit and contested — that the operation claims to capture; the value is a claim about this, not a bare number. A scale (the codomain). A numerical, categorical, or ordinal scale onto which the attribute is mapped; its type (nominal, ordinal, interval, ratio) fixes which downstream operations are meaning-preserving.

    This sourceIntroduces the nominal/ordinal/interval/ratio classification fixing which operations are meaning-preserving for each scale type; the canonical source for scale-type-versus-admissible-operations and for reliability/validity as distinct properties.

• Qualitative property
  • This conserved decision sequence is the basis for Prime status.

Domain-specific

• Measurement Scale
  • Stevens's influential typology distinguishes nominal, ordinal, interval, and ratio scales by the empirical relations represented and transformations that leave scale statements invariant.

    This sourceIntroduces nominal, ordinal, interval, and ratio scale types through their defining operations and admissible transformations.

Mechanisms

• Dependence-Measure Selection Matrix
  • The whole apparatus rests on getting the variables' level of measurement right in the first place.

    This sourceEstablishes that legitimate statistical operations depend on whether variables are nominal, ordinal, interval, or ratio scaled.

• Rank-Based Methods
  • Where S. S. Stevens' scale of measurement types marks the line between ordinal and interval data, rank methods let an analysis live honestly at the ordinal level instead of borrowing interval precision the measurement never had.

    This sourceDistinguishes ordinal rank information from interval-scale precision and cautions against statistics that assume more than rank order.

Verification

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