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Accuracy vs. Precision

Two words used as synonyms in everyday speech — and two quite different things in the laboratory.

Most people believe accuracy and precision mean the same thing. But the two concepts are quite different.

The precision of an experiment is a measure of the reproducibility of it for multiple measurements. It is usually described by the standard deviation, standard error, or confidence interval.

The accuracy of an experiment is a measure of how closely the experimental results agree with the true value. Determining the accuracy of a measurement requires calibration of the method against a known standard.

In presence of a systematic error a measurement can be precise, but not accurate.

Seen on a distribution

Value Probability density Reference value Accuracy Precision
Repeated measurements form a distribution. Accuracy is the distance between the reference (true) value and the centre of that distribution; precision is how narrow the distribution is. The two are independent — a narrow curve sitting in the wrong place is precise but inaccurate.

Seen on a target

Precision the area covered by the scatter of the hits Accuracy the distance of the group from the centre
The Bull's Eye cartoon of the original note: the hits are tightly grouped — high precision — but the group sits well away from the centre. This is exactly what a systematic error looks like.

All four combinations are possible, and it is worth having them in mind together:

accurateand precise precise,not accurate accurate,not precise neither
Note the second case: a tight, repeatable cluster far from the centre. Precision alone is never evidence of correctness — only calibration against a known standard establishes accuracy.

Adapted from P. R. Bevington & D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill. Figures redrawn as vector graphics from the original NEMEX note.