Concept Architecture
Concept
Theoretically, Ordinal Scaling is a level of measurement in which observations are ranked according to magnitude or order without assuming equal intervals between adjacent categories. It is founded on classical measurement theory and permits meaningful comparison of relative position but not the magnitude of differences between observations. Within health economics, ordinal scaling is widely used in symptom severity scales, disease classifications and health-related quality of life instruments before preference weighting.
Mathematically, ordinal scaling is represented by an ordered set of categories in which only the ranking of observations is meaningful. The mathematical framework preserves order under any monotonic transformation but does not support arithmetic operations such as addition, subtraction, multiplication or division because the distances between categories are unknown.
In practice, ordinal scaling is implemented using ordered response categories such as ""none"", ""mild"", ""moderate"" and ""severe"" or numerical ranks such as 1 to 5. Analyses commonly use medians, percentiles, contingency tables and non-parametric statistical methods. Many preference-based health measures begin with ordinal responses that are subsequently transformed into utility values using validated value sets.
Purpose
Used to classify observations into ordered categories, enabling comparison of relative ranking where the magnitude of differences between categories cannot be assumed.
Mathematical Formulae
Primary Formula
There is no universally recognised canonical mathematical formula.
Supporting Formulae
For two observations x? and x?:
x? > x?
indicates that observation i ranks higher than observation j, without implying the size of the difference.
Related Mathematical Methods
- Classical measurement theory
- Stevens' theory of measurement scales
- Rank ordering
- Non-parametric statistics
- Monotonic transformation
Example
Patients rate pain using a four-level scale: 1 = none, 2 = mild, 3 = moderate and 4 = severe. A patient with a score of 4 has more severe pain than a patient with a score of 2, but it cannot be concluded that the pain is twice as severe because the intervals between categories are not defined.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| RANK.AVG | =RANK.AVG(B2,$B$2:$B$101) | Ranks observations on an ordinal scale. |
| MEDIAN | =MEDIAN(B2:B101) | Calculates the median ordinal response. |
| MODE.SNGL | =MODE.SNGL(B2:B101) | Identifies the most frequently reported category. |
| COUNTIF | =COUNTIF(B2:B101,4) | Counts respondents in a specified ordinal category. |
VBA (Optional)
Automate the summarisation of ordinal responses by producing frequency tables, medians and rank-based descriptive statistics.
Sources
- Stevens SS. On the Theory of Scales of Measurement. Science. 1946;103:677?680.
- Agresti A. Analysis of Ordinal Categorical Data. Wiley.
- Brazier J, Ratcliffe J, Salomon JA, Tsuchiya A. Measuring and Valuing Health Benefits for Economic Evaluation. Oxford University Press.
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
Related Concepts (2)
Library
Publications
1
Measuring and Valuing Health Benefits for Economic Evaluation — Brazier, Ratcliffe, Salomon & Tsuchiya, 2nd Edition ed., 2017 (Oxford University Press)
The comprehensive text on the measurement and valuation of health benefits for economic evaluation — defining health, valuation techniques (time trade-off, standard gamble), whose values to use, preference-based measures (EQ-5D, SF-6D), and the construction of QALYs.
BookView source →
Frequently Asked Questions (6)
What is ordinal scaling?
A measurement scale property in which values can be ranked but numerical differences do not necessarily reflect equal differences in the underlying quantity.
Source: Torrance GW. Measurement of health state utilities for economic appraisal. Journal of Health Economics. 1986;5(1):1-30. doi:10.1016/0167-6296(86)90020-2.
What is an example of an ordinal scale in health?
Many familiar health gradings are ordinal. Cancer stages from one to four, a pain rating running from mild to severe, and disease-severity classes all place patients in ordered categories without implying that the step from one category to the next is the same size as any other. The order carries meaning but the spacing does not, so the interval between stage one and stage two need not equal that between stage three and stage four. Stevens (1946) classified such rankings as ordinal.
Source: Stevens 1946
What can and cannot be done with ordinal data?
Ordinal data support statements of order, that one item ranks above another, and operations that depend only on rank, such as medians and rank correlations, but they do not support arithmetic that assumes equal intervals, such as adding values or computing meaningful means, since the differences between values are not defined. Treating ordinal values as if their intervals were equal can mislead, so the analysis is confined to what order alone justifies.
Source: Torrance 1986
Why is ordinal scaling insufficient for utilities?
Ordinal scaling is insufficient for utilities because quality-adjusted life years weight time by utility and sum across states, operations that require equal differences in utility to represent equal differences in health, which an ordinal scale does not guarantee. A ranking of health states shows only their order, not by how much one is better than another, so it cannot support the arithmetic of economic evaluation. Utilities therefore need at least interval-level, not merely ordinal, measurement.
Source: Torrance 1986
How does ordinal scaling relate to ranking methods?
Ranking methods, such as paired comparison or simple ordering of health states, produce ordinal data, showing which states are preferred to others but not by how much. To yield utilities, this ordinal information must be converted to at least an interval scale, for instance by modelling the ranks under assumptions that recover cardinal values, as discrete choice experiments do. Ranking alone establishes order, which is a starting point but not a utility.
Source: Torrance 1986
How does ordinal scaling differ from interval and ratio scaling?
Ordinal scaling conveys only order, interval scaling adds equal and meaningful differences between values, and ratio scaling adds a true zero allowing meaningful ratios. Ranking states is ordinal; assigning values whose differences are equal for equal health changes is interval; a scale on which one value can be said to be twice another is ratio. Economic evaluation requires at least interval-level utilities, so ordinal information must be scaled up before it can be used.
Source: Torrance 1986
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 1 Sep 2025
Content version: 1.0.0
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- Persistent URI
- https://healtheconomics.wiki/concept/ordinal-scaling
- Term code
- HE-EE-HU-054
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