Slide 1
A calculated area inherits uncertainty from its measurements
An area calculated from measured length and width is not exact. Uncertainty in both measurements affects the reported area.
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A measurement model states how the desired quantity depends on inputs. Writing that relationship first helps identify overlooked influences, such as thermal expansion when a dimension changes with temperature.
Slide 2
Sensitivity determines which input matters most
Sensitivity describes how strongly an output changes when one input changes. Equal input uncertainties need not have equal effects.
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For a rectangle, changing its length by a millimetre changes area more when the width is large. The physical relationship, rather than the number of decimal places, determines that influence.
Slide 3
Independent uncertainties can combine through squares
Independent standard uncertainties often combine through a square-root-of-squares calculation. Adding every uncertainty directly answers a different, more conservative question.
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For a sum of independent inputs with standard uncertainties of 3 and 4 units, the combined standard uncertainty is 5 units. This example assumes the sensitivity to each input is one.
Slide 4
Shared references can make errors move together
Two measurements made with the same reference may have correlated errors. Their uncertainty contributions cannot always be treated as independent.
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A shared scale error can partly cancel in a ratio, while reinforcing in a sum. Covariance expresses this connection mathematically; ignoring it can make an uncertainty estimate too large or too small.
Slide 5
The reported interval needs a stated meaning
A reported uncertainty needs a defined meaning and method. An interval without context does not reveal how it was constructed.
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Expanded uncertainty multiplies a combined standard uncertainty by a coverage factor. Interpreting that factor as a probability also requires assumptions about the distribution and available information; it is not automatic for every measurement.
Sources
- Measurement Uncertainty
National Institute of Standards and Technology
- Law of Propagation of Uncertainty
National Institute of Standards and Technology