Problem
Explain the difference between precision and accuracy using the target analogy: which of the four patterns (A, B, C, D) corresponds to the cases precise-accurate, precise-not-accurate, accurate-not-precise, neither one nor the other?
Solution
The two definitions. In the target analogy the centre represents the true value.
- Accuracy measures how close the shots are to the centre: the more the shots fall around the true value, the more accurate the measurement. A lack of accuracy signals a systematic error.
- Precision measures how close together the shots are, regardless of where they fall: tight shots = precise measurement, scattered shots = imprecise measurement. The spread reflects the random error.
Reading the four patterns.
- A → precise and accurate. The shots are both close together and centred on the true value: small random error and small systematic error. This is the ideal situation.
- B → precise but not accurate. The shots are well grouped (high precision) but all shifted to the same side of the centre: there is a clear systematic error (for example, an uncalibrated instrument).
- C → accurate but not precise. The shots are scattered (low precision) but distributed around the centre, so that their mean falls close to the true value: a lot of random error, little systematic error.
- D → neither precise nor accurate. The shots are both scattered and far from the centre: large random error and large systematic error.
Remark. Precision and accuracy are independent: one can be very precise and completely inaccurate (case B). Repeating measurements and averaging improves the estimate when the error is random (it brings C closer to A), but it does not correct a systematic error (B stays shifted).
Links
Topics: Metodo sperimentale Concepts: Cifre significative e incertezza