Accuracy vs precision in measurement

A sensor that reads 24.9, 24.9, 25.0, 24.9 °C when the true value is 21.0 °C is precise and inaccurate. One that reads 20.6, 21.5, 20.8, 21.2 °C is imprecise but, on average, close. The first can be fixed by a correction from calibration; the second only by a better sensor or by averaging.

How the concepts map to a budget

• Random effects (precision) enter as Type A repeatability.
• Systematic effects are corrected where known; the uncertainty of the correction enters as Type B.
• Uncorrected systematic effects are treated as uncertainty components, not ignored.

Marketing copy uses 'accuracy' for a specification limit. Metrology uses uncertainty. When comparing instruments, ask what the number is and under which conditions it holds.

Four instruments, one true value

The distinction is easiest to see with the cases laid side by side. In each row below the true value is 21.0 °C and the instrument has been read four times.

The second row is the important one, because it is the case people expect calibration to solve and it cannot. A correction shifts every reading by the same amount; it does nothing about scatter. Scatter is reduced only by averaging more readings, by removing the cause, or by a better instrument.

Trueness, which is the word that is missing

The VIM gives three terms where ordinary speech gives two. Precision is closeness of agreement between repeated measurements — scatter. Trueness is closeness of agreement between the average of many measurements and a reference value — offset. Accuracy is closeness of a single measured value to the true value, and it therefore combines both. That is why the GUM discourages using accuracy as a number at all: quoting accuracy: ± 0.5 °C is stating a maximum permissible error, not an accuracy.

How each reaches the budget

• Random effects — the scatter — enter as a Type A repeatability component, evaluated as the standard deviation of repeated readings.
• Known systematic effects are corrected. The correction is applied to the result and its own uncertainty enters as a Type B component. Applying a correction never removes uncertainty entirely; it replaces a large known error with a small unknown one.
• Systematic effects known to exist but not corrected are treated as uncertainty components with an estimated bound — a legitimate choice, but a larger one.
• Effects nobody has identified show up as the gap between repeatability and intermediate precision, which is the argument for measuring both.

When comparing two instruments on their specification sheets, the question to ask is what the number is and under what conditions it holds. A ± 0.3 °C figure at 23 °C ambient after 30 minutes of warm-up is not comparable with a ± 0.5 °C figure over the full operating range.