Concept Architecture
Concept
Theoretically, an Outlier is an observation that differs markedly from the remainder of a dataset and is inconsistent with the expected pattern of variation under the assumed statistical model. Outliers may arise from measurement error, data entry error, natural biological variability or genuinely extreme observations. The concept exists because unusually large or small observations can substantially influence statistical estimation, model fitting and inference, particularly for methods that depend on means and variances.
Mathematically, outliers are identified using recognised statistical criteria based on distances, residuals or probability distributions rather than a single universal definition. Common approaches include standardised or studentised residuals, z-scores, the interquartile range rule, Cook's Distance and Mahalanobis Distance. Different methods are appropriate depending on whether the analysis concerns univariate data, regression models or multivariate observations.
In practice, outlier detection is performed during exploratory data analysis and regression diagnostics before fitting or interpreting statistical models. In health economics, outliers frequently occur in healthcare costs, hospital length of stay, resource utilisation and treatment expenditures because a small number of patients may incur exceptionally high costs. Analysts should investigate the origin of outliers and determine whether they represent data errors or genuine observations before deciding on exclusion, transformation or robust statistical methods.
Purpose
Used to identify unusually extreme observations, assess their influence on statistical analyses, improve model diagnostics and support robust estimation in health economic research.
Mathematical Formulae
Primary Formula
Standardised z-score:
z = (x ? ?) / �
Observations are commonly investigated when:
|z| > 3
Supporting Formulae
Interquartile Range (IQR) rule:
Lower Bound = Q? ? 1.5 ? IQR
Upper Bound = Q? + 1.5 ? IQR
where:
IQR = Q? ? Q?
Mahalanobis Distance:
D� = (x ? ?)?�??(x ? ?)
Cook's Distance:
D? = [e?� / (p ? MSE)] ? [h?? / (1 ? h??)�]
Related Mathematical Methods
- Studentised Residuals
- Standardised Residuals
- Cook's Distance
- Mahalanobis Distance
- Interquartile Range
- Robust Regression
- Leverage Point
Example
A health economist analyses annual healthcare costs for 2,000 patients.
The summary statistics are:
- Mean cost = �4,200
- Standard deviation = �1,100
One patient incurs healthcare costs of �8,000.
The corresponding z-score is:
z = (8,000 ? 4,200) / 1,100
z = 3.45
Because the absolute z-score exceeds 3, the observation is investigated further. Clinical review confirms that the patient experienced multiple intensive care admissions. The observation is therefore retained, and robust sensitivity analyses are performed to assess its influence on the economic evaluation.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| STANDARDIZE | =STANDARDIZE(B2,$H$2,$H$3) | Calculate z-scores for healthcare costs or outcomes. |
| QUARTILE.INC | =QUARTILE.INC(B2:B2001,1) | Calculate the first and third quartiles for the IQR method. |
| IF | =IF(ABS(C2)>3,"Potential Outlier","Typical Observation") | Flag extreme observations using z-score thresholds. |
| ABS | =ABS(C2) | Calculate the absolute standardised distance from the mean. |
| PERCENTILE.INC | =PERCENTILE.INC(B2:B2001,0.75) | Calculate percentile cut-offs for exploratory outlier detection. |
VBA (Optional)
A VBA routine can automatically identify potential outliers using multiple diagnostic criteria, generate summary reports and flag influential observations for further investigation.
Sources
- Barnett V, Lewis T. Outliers in Statistical Data. Wiley.
- Rousseeuw PJ, Leroy AM. Robust Regression and Outlier Detection. Wiley.
- Cook RD, Weisberg S. Residuals and Influence in Regression. Chapman & Hall.
- Belsley DA, Kuh E, Welsch RE. Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. Wiley.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
- Drummond MF, et al. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
Related Concepts (2)
Library
Publications
1
Bayesian Methods in Health Economics — Gianluca Baio, 1st Edition ed., 2012 (Chapman & Hall / CRC Press)
An overview of Bayesian statistical methods for the analysis of health economic data, covering economic evaluation concepts, statistical cost-effectiveness analysis, Bayesian computation and MCMC, and applied health economic evaluation.
BookView source →
Frequently Asked Questions (6)
What is an outlier?
An observation differing markedly from other values in a dataset, either from genuine unusual variation or a measurement or entry error.
Source: Grubbs 1969
What marks an observation as an outlier?
An outlier is an observation that stands far apart from the rest of the data, its value markedly higher or lower than the general pattern. It may arise from genuine but unusual variation, such as a truly extreme patient, or from an error in measurement or data entry, and telling these apart matters before deciding what to do. Outliers deserve attention because they can distort summaries such as the mean and pull a fitted model toward themselves. A value far outside the pack is what defines it. Kirkwood and Sterne (2003) describe this.
Source: Kirkwood & Sterne 2003
How are outliers detected?
Outliers are detected by graphical methods such as box plots and scatterplots, which display values far from the rest; by rules based on distance from the centre, such as values beyond a number of standard deviations or outside the interquartile range by a set multiple; and by formal tests such as Grubbs' test. So outliers are detected through a combination of visual inspection and numerical rules or tests that identify values unusually distant from the others, which flags them for examination, though detection methods provide guidance rather than definitive judgement, since whether a flagged value is a genuine extreme or an error requires investigation of its origin.
Source: Grubbs 1969
What causes outliers?
Outliers can be caused by genuine variability, where the observation is a real but atypical value reflecting true diversity in the population; by measurement error, where the value is recorded inaccurately; or by data entry or processing errors, where mistakes produce implausible values. So outliers arise from either real unusual cases or errors, and distinguishing between these causes is important, since a genuine outlier carries real information and should generally be retained, whereas an erroneous one should be corrected or removed, which is why identifying the cause, rather than treating all outliers alike, is central to handling them appropriately.
Source: Grubbs 1969
How should outliers be handled?
Outliers should be handled by first investigating their cause: if an outlier results from an error, it should be corrected or removed, while a genuine outlier reflecting real variation should generally be retained, though its influence on the analysis may be examined and robust methods considered. So outliers are handled by understanding why they occur rather than automatically deleting them, since removing genuine extreme values can bias the analysis and discard information, whereas retaining errors can distort it, which is why the response depends on the cause, and sensitivity analyses or robust methods are used to assess and limit the impact of outliers of uncertain origin.
Source: Grubbs 1969
Why do outliers matter?
Outliers matter because they can strongly influence statistical analyses, particularly those based on means, variances, and least-squares methods, so that a single extreme value can distort estimates, inflate variability, or drive a regression, potentially misleading conclusions. So outliers matter for the robustness and validity of an analysis, since results unduly influenced by a few extreme values may not reflect the general pattern, which is why outliers are detected and investigated, their cause determined, and their impact assessed, using robust methods where appropriate, to ensure that the analysis represents the data as a whole rather than being dominated by atypical points.
Source: Grubbs 1969
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 19 Dec 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/outlier
- Term code
- HE-ES-SA-144
Stable URI · Machine-readable · Resolvable · CC BY 4.0