Concept Architecture
Concept
Theoretically, Absolute Error is a mathematical measure that quantifies the magnitude of the difference between an observed or estimated value and its true or reference value. It is one of the most fundamental measures of numerical accuracy and is widely used in numerical analysis, statistics, optimisation and scientific computing. Unlike signed error, Absolute Error ignores the direction of the deviation and measures only its size.
Mathematically, Absolute Error is defined as the absolute value of the difference between the true value and the estimated value. Because it is always non-negative, it provides a direct measure of approximation accuracy regardless of whether the estimate overestimates or underestimates the true quantity. Absolute Error forms the basis of numerous aggregate error measures, including Mean Absolute Error (MAE).
In practice, Absolute Error is used in health economics to assess prediction accuracy, evaluate regression and simulation models, compare forecasting methods and validate numerical approximations. It is applied in cost prediction, survival modelling, epidemiological forecasting and economic evaluation to quantify the accuracy of estimated outcomes.
Purpose
Used to quantify the magnitude of estimation error, evaluate prediction accuracy, compare numerical methods and support validation of statistical and health economic models.
Mathematical Formulae
Primary Formula
Absolute Error = |True Value ? Estimated Value|
or
AE = |x ? x?|
where:
- x = true value
- x? = estimated value
Supporting Formulae
Mean Absolute Error
MAE = (1 � n) �|x? ? x??|
Relative Absolute Error
RAE = |x ? x?| � |x|
Related Mathematical Methods
- Mean Absolute Error
- Relative error
- Prediction error
- Root Mean Square Error
- Least squares approximation
- Numerical analysis
Example
The true healthcare cost is �2,500, while a prediction model estimates �2,350.
Absolute Error
= |2,500 ? 2,350|
= �150
The prediction therefore has an Absolute Error of �150, regardless of whether the estimate is above or below the true value.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| ABS | =ABS(A2-B2) | Calculate the Absolute Error for a prediction. |
| AVERAGE | =AVERAGE(C2:C101) | Calculate the average Absolute Error. |
| SUM | =SUM(C2:C101) | Calculate the total Absolute Error across observations. |
| IF | =IF(ABS(A2-B2)<=100,"Acceptable","Review Model") | Assess prediction accuracy against a predefined threshold. |
| ABS/TRUE | =ABS(A2-B2)/A2 | Calculate the Relative Absolute Error. |
VBA (Optional)
Automate calculation of Absolute Error across prediction models, simulation outputs and forecasting analyses while generating model validation reports and performance dashboards.
Sources
- Burden RL, Faires JD. Numerical Analysis.
- Atkinson KE. An Introduction to Numerical Analysis.
- Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical Recipes: The Art of Scientific Computing.
- Hastie T, Tibshirani R, Friedman J. The Elements of Statistical Learning.
- 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 (6)
Library
Publications
1
Accuracy and Stability of Numerical Algorithms — Nicholas J. Higham, 2nd Edition ed., 2002 (Society for Industrial and Applied Mathematics (SIAM))
The standard reference on floating-point error, conditioning, stability and the numerical reliability of matrix, polynomial and linear-algebra algorithms.
BookView source →
Frequently Asked Questions (6)
What is absolute error?
The absolute difference between an estimated or measured value and the true or accepted value.
Source: NIST Digital Library of Mathematical Functions. Chapter 3: Numerical Methods.
What does absolute error measure?
Absolute error measures the absolute difference between an estimated or measured value and the true or accepted value, so it reports the size of the discrepancy in the same units as the quantity itself. Because it keeps the original units, absolute error states how far an estimate lies from the reference value without scaling that gap to the value's magnitude. This makes absolute error a direct measure of the raw deviation between an estimate and the truth Because it is reported in the quantity's own units, absolute error is straightforward to interpret but must be read against the scale of the value to judge whether the deviation is large or small.
Source: NIST Digital Library of Mathematical Functions. Chapter 3: Numerical Methods.
Why does absolute error take the absolute value of the difference?
Absolute error takes the absolute value so that the discrepancy is reported as a non-negative magnitude regardless of whether the estimate is too high or too low. By discarding the sign, absolute error focuses on the size of the deviation between an estimated or measured value and the true or accepted value rather than its direction. This means two estimates that miss the true value by the same amount in opposite directions share the same absolute error Because it is reported in the quantity's own units, absolute error is straightforward to interpret but must be read against the scale of the value to judge whether the deviation is large or small.
Source: NIST Digital Library of Mathematical Functions. Chapter 3: Numerical Methods.
In what units is absolute error expressed?
Absolute error is expressed in the same units as the quantity being estimated, because it is simply the absolute difference between an estimated or measured value and the true or accepted value. Keeping the original units lets absolute error be read directly, but it also means the figure cannot be compared meaningfully across quantities of very different scale. For that reason absolute error is often reported alongside a scaled measure when comparability across quantities matters Because it is reported in the quantity's own units, absolute error is straightforward to interpret but must be read against the scale of the value to judge whether the deviation is large or small.
Source: NIST Digital Library of Mathematical Functions. Chapter 3: Numerical Methods.
What is a limitation of absolute error?
A limitation of absolute error is that, being the absolute difference between an estimated value and the true value in raw units, it gives no sense of how large the deviation is relative to the quantity itself. An absolute error of one unit is negligible against a true value of a million but severe against a true value of two. Absolute error therefore describes the raw gap but not its proportional importance Because it is reported in the quantity's own units, absolute error is straightforward to interpret but must be read against the scale of the value to judge whether the deviation is large or small.
Source: NIST Digital Library of Mathematical Functions. Chapter 3: Numerical Methods.
How does absolute error relate to relative error?
Absolute error is the absolute difference between an estimated or measured value and the true or accepted value, while relative error expresses that same absolute error as a proportion or percentage of the true value. Relative error is therefore derived from absolute error by scaling it to the magnitude of the quantity. The two measures are complementary, with absolute error giving the raw size of the deviation and relative error giving its proportional size Because it is reported in the quantity's own units, absolute error is straightforward to interpret but must be read against the scale of the value to judge whether the deviation is large or small.
Source: NIST Digital Library of Mathematical Functions. Chapter 3: Numerical Methods.
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 1 Jul 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/absolute-error
- Term code
- CS-NA-EA-001
Stable URI · Machine-readable · Resolvable · CC BY 4.0