Concept Architecture
Concept
Theoretically, Percentile is a descriptive statistical measure that indicates the value below which a specified percentage of observations in an ordered dataset falls. It provides a rank-based summary of the distribution of data and is widely used to describe the relative position of an individual observation within a population or sample. Percentiles are fundamental to non-parametric statistics and exploratory data analysis because they do not require assumptions about the underlying distribution.
Mathematically, percentiles are obtained by ordering observations and identifying the value corresponding to a specified cumulative proportion of the dataset. Various estimation methods exist for calculating percentiles from finite samples, differing primarily in their interpolation procedures. The pth percentile corresponds to the value at which p% of observations are less than or equal to that value.
In practice, percentiles are calculated from ordered observations using recognised statistical algorithms implemented in statistical software. In health economics they are commonly used to summarise skewed distributions of healthcare costs, waiting times, resource utilisation, willingness-to-pay values, and uncertainty distributions generated by probabilistic sensitivity analysis.
Purpose
Used to describe the relative position of observations within a distribution, summarise skewed data, identify thresholds, compare populations, and report uncertainty in health economic analyses.
Mathematical Formulae
Primary Formula
L = (p / 100) ? (n + 1)
where:
- L = percentile position
- p = desired percentile
- n = number of observations
Supporting Formulae
If L is an integer:
P? = x(L)
If L lies between two ordered observations:
P? = x(k) + (L ? k) ? [x(k + 1) ? x(k)]
where k = ?L?.
Related Mathematical Methods
- Quantiles
- Quartiles
- Deciles
- Interquartile Range
- Order Statistics
- Empirical Distribution Function
- Non-Parametric Statistics
Example
Annual healthcare costs are recorded for 200 patients. The ordered data indicate that the position of the 90th percentile is:
L = (90 / 100) ? (200 + 1)
L = 180.9
The 90th percentile is obtained by interpolating between the 180th and 181st ordered observations. If these values are �14,800 and �15,000 respectively:
P?? = �14,800 + 0.9 ? (�15,000 ? �14,800)
P?? = �14,980
This indicates that 90% of patients incurred annual healthcare costs of �14,980 or less.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| PERCENTILE.INC | =PERCENTILE.INC(B2:B201,0.90) | Calculate the 90th percentile of healthcare costs. |
| PERCENTILE.EXC | =PERCENTILE.EXC(B2:B201,0.90) | Estimate percentiles using the exclusive method. |
| QUARTILE.INC | =QUARTILE.INC(B2:B201,3) | Calculate the upper quartile of cost or utility data. |
| SORT | =SORT(B2:B201) | Order observations prior to manual percentile calculations. |
| RANK.AVG | =RANK.AVG(B2,$B$2:$B$201) | Determine the relative ranking of individual observations. |
VBA (Optional)
Automate percentile calculations across multiple health economic outcome variables and generate percentile summary tables for reporting.
Sources
- Hyndman RJ, Fan Y. Sample Quantiles in Statistical Packages. The American Statistician. 1996.
- Altman DG. Practical Statistics for Medical Research.
- Conover WJ. Practical Nonparametric Statistics.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
- Drummond MF, et al. Methods for the Economic Evaluation of Health Care Programmes.
- NICE Health Technology Evaluation Manual.
Related Concepts (2)
Library
Publications
1
Statistical Analysis of Cost-Effectiveness Data — Willan & Briggs, 1st Edition ed., 2006 (John Wiley & Sons)
A synthesis of statistical methods for analysing cost-effectiveness data, including net-benefit regression, confidence intervals for the ICER, cost-effectiveness acceptability curves, and covariate adjustment. Part of the Wiley Statistics in Practice series.
BookView source →
Frequently Asked Questions (6)
What is a percentile?
A descriptive statistic indicating the value below which a specified percentage of observations in a dataset fall.
Source: Casella G, Berger RL. Statistical Inference. 2nd ed. Duxbury; 2002.
What does a percentile reveal about a value's position?
A percentile indicates where a value stands within a distribution by giving the percentage of observations that fall below it. A measurement at the ninetieth percentile, for example, exceeds ninety per cent of the others, which locates it near the top without any need for the actual figures. This makes percentiles a clear way to describe relative standing, widely used for growth charts and reference ranges. Quartiles and deciles are simply particular percentiles. Marking a value's rank in the distribution is what it does. Kirkwood and Sterne (2003) describe this.
Source: Kirkwood & Sterne 2003
How is a percentile calculated?
A percentile is calculated by ordering the data and finding the value below which the specified percentage of observations fall, with interpolation between values used when the exact position lies between data points; several conventions exist for the precise method. So a percentile is calculated from the ordered data by locating the point corresponding to the desired percentage, which identifies the value beneath which that fraction of the data lies, and because different interpolation rules can give slightly different results, the method used is sometimes specified, though for large datasets the differences are minor and the percentile reliably indicates the position within the distribution.
Source: Casella & Berger 2002
What are percentiles used for?
Percentiles are used to describe the position of a value within a distribution, to summarise spread through percentiles such as the quartiles, and to establish reference ranges, such as growth charts where a child's measurement is compared with population percentiles. So percentiles are used to convey where observations stand relative to a distribution and to define normal or reference ranges, which is valuable in clinical contexts such as growth and laboratory reference values, and in describing distributions, since reporting selected percentiles captures the spread and shape of data in a way that is robust and easy to interpret.
Source: Casella & Berger 2002
How do percentiles relate to quartiles and deciles?
Percentiles relate to quartiles and deciles as finer divisions of the same kind: percentiles divide ordered data into hundredths, quartiles into four equal parts, and deciles into ten, so quartiles and deciles correspond to specific percentiles, the quartiles to the twenty-fifth, fiftieth, and seventy-fifth percentiles and the deciles to every tenth percentile. So percentiles, quartiles, and deciles are all quantiles dividing data into equal parts, differing in the number of divisions, with percentiles the finest, and they are used according to how detailed a description of the distribution's positions is required.
Source: Casella & Berger 2002
Why are percentiles useful?
Percentiles are useful because they describe the distribution and the position of values in a way that is robust to the shape of the data and to outliers, being based on rank, and they are readily interpretable, conveying the percentage of data below a value. So percentiles are useful for summarising distributions and locating observations without assuming a particular distributional form, which makes them valuable for skewed data and for reference ranges, since knowing that a value lies at a given percentile immediately conveys its standing relative to the rest, and percentiles underpin robust measures of spread such as the interquartile range.
Source: Casella & Berger 2002
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 22 Dec 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/percentile
- Term code
- HE-ES-SA-156
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