Experimental uncertainty analysis is a technique that analyses a ''derived'' quantity, based on the uncertainties in the experimentally ''measured'' quantities that are used in some form of mathematical relationship ("
model
A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure.
Models c ...
") to calculate that derived quantity. The model used to convert the measurements into the derived quantity is usually based on fundamental principles of a
science
Science is a systematic endeavor that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe.
Science may be as old as the human species, and some of the earli ...
or
engineering
Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...
discipline.
The uncertainty has two components, namely, bias (related to ''
accuracy
Accuracy and precision are two measures of ''observational error''.
''Accuracy'' is how close a given set of measurements ( observations or readings) are to their ''true value'', while ''precision'' is how close the measurements are to each oth ...
'') and the unavoidable
random variation that occurs when making repeated measurements (related to ''
precision
Precision, precise or precisely may refer to:
Science, and technology, and mathematics Mathematics and computing (general)
* Accuracy and precision, measurement deviation from true value and its scatter
* Significant figures, the number of digit ...
''). The measured quantities may have
biases
Bias is a disproportionate weight ''in favor of'' or ''against'' an idea or thing, usually in a way that is closed-minded, prejudicial, or unfair. Biases can be innate or learned. People may develop biases for or against an individual, a group, ...
, and they certainly have
random variation, so what needs to be addressed is how these are "propagated" into the uncertainty of the derived quantity. Uncertainty analysis is often called the "
propagation of error
In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of ex ...
."
Introduction
For example, an experimental
uncertainty analysis of an undergraduate physics lab experiment in which a
pendulum
A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward th ...
can estimate the value of the local
gravitational acceleration
In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag). This is the steady gain in speed caused exclusively by the force of gravitational attraction. All bodi ...
constant ''g''. The relevant equation
[The exact period requires an elliptic integral; see, e.g., This approximation also appears in many calculus-based undergraduate physics textbooks.] for an idealized simple pendulum is, approximately,
: