Concept Architecture
Concept
Theoretically, Variation is the statistical concept describing the extent to which observations differ from one another or from a central value within a population or sample. It is a fundamental property of all measured data and forms the basis of statistical inference, probability theory and quality improvement. In health economics, variation reflects differences in health outcomes, healthcare utilisation, costs and clinical performance arising from biological, behavioural, environmental or system-level factors.
Mathematically, variation is quantified using measures of dispersion that describe the spread of observations around a measure of central tendency. Common measures include the variance, standard deviation, range, interquartile range and coefficient of variation. The choice of measure depends on the distribution of the data and the objectives of the analysis.
In practice, variation is analysed to distinguish expected random fluctuations from meaningful differences requiring intervention. Health economists use measures of variation to evaluate uncertainty, assess heterogeneity between populations, monitor healthcare quality, compare provider performance and support statistical modelling and economic evaluation.
Purpose
Used to quantify the spread of observations, assess uncertainty, compare populations or processes, identify meaningful differences and support statistical, epidemiological and health economic analyses.
Mathematical Formulae
Primary Formula
Population Variance
�� = �(x? ? ?)� � N
Population Standard Deviation
� = �[�(x? ? ?)� � N]
Supporting Formulae
Sample Variance
s� = �(x? ? x?)� � (n ? 1)
Coefficient of Variation
CV = (� � ?) ? 100%
Range
Range = Maximum ? Minimum
Related Mathematical Methods
- Variance
- Standard deviation
- Coefficient of variation
- Interquartile range
- Analysis of variance
- Statistical process control
Example
Five hospitals report average lengths of stay of 4, 5, 6, 5 and 10 days.
Mean = 6 days
Population Variance
�� = [(4?6)� + (5?6)� + (6?6)� + (5?6)� + (10?6)�] � 5
= (4 + 1 + 0 + 1 + 16) � 5
= 4.4
Standard Deviation
� = �4.4
= 2.10 days
The data therefore exhibit measurable variation, indicating differences in hospital performance that may warrant further investigation.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| VAR.S | =VAR.S(A2:A101) | Calculate sample variance. |
| STDEV.S | =STDEV.S(A2:A101) | Calculate sample standard deviation. |
| MAX-MIN | =MAX(A2:A101)-MIN(A2:A101) | Calculate the range of observations. |
| QUARTILE.INC | =QUARTILE.INC(A2:A101,3)-QUARTILE.INC(A2:A101,1) | Calculate the interquartile range. |
| STDEV.S/AVERAGE | =(STDEV.S(A2:A101)/AVERAGE(A2:A101))*100 | Calculate the coefficient of variation. |
VBA (Optional)
Automate calculation of measures of variation across healthcare datasets while generating statistical summaries, quality monitoring reports and health economic performance dashboards.
Sources
- Casella G, Berger RL. Statistical Inference.
- Rice JA. Mathematical Statistics and Data Analysis.
- Montgomery DC, Runger GC. Applied Statistics and Probability for Engineers.
- Rothman KJ, Greenland S, Lash TL. Modern Epidemiology.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes.
Related Concepts (2)
Frequently Asked Questions (6)
What is variation?
Differences observed in a healthcare process or outcome across patients, providers, or time periods, either legitimate or reflecting inconsistent quality.
Source: Shewhart 1931
What differences in a process or outcome is variation?
Variation is differences observed in a healthcare process or outcome. It describes how a process or its results differ, rather than staying uniform. It is observed across patients, providers, or time periods, wherever comparable things turn out differently. It can be legitimate, reflecting real differences in need, or it can reflect inconsistent quality, differences that should not exist. It splits into warranted and unwarranted variation, the justified and the unjustified kinds. Differences in a process or its results is what it names. Shewhart (1931) set out the study of variation.
Source: Shewhart 1931
What does variation describe?
Variation describes differences observed in a healthcare process or outcome, so it captures how a process or outcome differs across patients, providers, or time periods, either legitimate or reflecting inconsistent quality. This description of differences defines it. So variation is differences observed in a healthcare process or outcome across patients, providers, or time periods, either legitimate or reflecting inconsistent quality This span across patients, providers, and time is what variation appears in for a healthcare process or outcome.
Source: Shewhart 1931
Across what is variation observed?
Variation is observed across patients, providers, or time periods, so the differences in a healthcare process or outcome appear among patients, among providers, or across time, either legitimate or reflecting inconsistent quality. This span across patients, providers, and time defines it. So variation is differences observed in a healthcare process or outcome across patients, providers, or time periods, either legitimate or reflecting inconsistent quality This range from legitimate to quality-reflecting is what variation covers in a healthcare process or outcome.
Source: Shewhart 1931
What can variation be?
Variation can be either legitimate or reflecting inconsistent quality, so the differences observed in a healthcare process or outcome may be legitimate or may signal inconsistent quality. This range from legitimate to quality-reflecting defines it. So variation is differences observed in a healthcare process or outcome across patients, providers, or time periods, either legitimate or reflecting inconsistent quality This relationship is what makes warranted and unwarranted variation the legitimate and illegitimate kinds of variation.
Source: Shewhart 1931
How does variation relate to warranted and unwarranted variation?
Variation relates to warranted and unwarranted variation as the general idea to its two kinds: variation is differences observed in a healthcare process or outcome, either legitimate or reflecting inconsistent quality, warranted variation is differences that appropriately reflect legitimate need, and unwarranted variation is differences unexplained by illness, preference, or evidence. So warranted and unwarranted variation are the legitimate and illegitimate kinds of variation, connected as its two forms.
Source: Shewhart 1931
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 30 Mar 2026
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/variation
- Term code
- HS-NHS-HQ-085
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