Difference between revisions of "Precision"

Latest revision as of 15:06, 6 October 2024

See also:

• Topological atomic precision
• Positional atomic precision

(wiki-TODO: Add the classic illustration of a dart board to illustrate precision and accuracy …)

Precision in the context of manipulation with actuators

(TODO: elaborate)

Precision in the context of measurements with sensors

Precision:

• The narrowness (linguistic use) or width (math use) of the random distribution in the (nowadays digital and discrete) measurement readout.
  Usually expressed in standard deviation, FWHM or similar.
• Not(!) the possibly present random distribution in the "real" value.
  (Note the problem of drawing the line betwene noise in the "real" value and noise in the measurement system!)
• inverse of random measurement deviation
• The unit of precision (when used in the linguistic sense) is the inverse of the measurement quantity
  ("more precise" <=> higher value of inverse standard deviation)
• Precision (of single measurements**) can never exceed (be finer than) resolution.

Precision sits on top of resolution!

Resolution:

• The size of the steps of the measurement readout (no further sub-steps).
• In case precision is far lower than resolution a one step difference is pretty meaningless.
• The unit of resolution is: readable steps per unit of measurement quantity
• Resolution is always higher than Precision (of single measurements**)

When precision closes in on resolution discretization error joins the party complicating things.

Accuracy: (trueness)

• how near the expectation value comes to a reference value ("true" value) - (a qualitative term?)
• inverse of the systematic measurement deviation

If accuracy is low highly precise measurements are consistently wrong.
An error that can be potentially compensated.

Lowering bandwidth to increase resolution and precision

By taking many measurements and averaging them out precision can be improved**. Measuring this way takes more time so the maximum frequency of measurements (bandwidth) gets lower. This is why noise in measurement readouts falls/(rises) with falling/(rising) bandwidth.

In case of manual averaging over many sub measurements at some point precision hits the resolution limit. Quite a bit before that happens one should start to store the averaged values with a higher resolution. While the new precision must still be higher than the new resolution (fundamental fact), the new higher precision (harbored in the new higher resolution) can exceed the old resolution.

The continuum:
Even a single measurement takes finite time. So it can be seen as an average over many much shorter sub measurements with much lower precision each. Higher bandwidth <=> more noise.

This is related to the Heisenberg uncertainty principle.
Note that in mechanical nanosystems at room temperature quantum "noise" can be significantly overpowered by thermal noise.

External links

Wikipedia

• en: Accuracy_and_precision => validity ~ seldom: Exactness
  (accuracy ~ seldom: correctness ~ ISO: trueness)
  de: Richtigkeit & Präzision => Genauigkeit ~ selten: Exaktheit ~ selten: Validität
  (Richtigkeit ~ selten: Akkuratheit)

• Random and systematic errors:
  Observational_error; Errors_and_residuals;
  de: Zufällige Abweichung & Systematische_Abweichung => Messabweichung

• Image_resolution
• Resolution (in various contexts); de: Auflösung
• Precision (in various contexts)

• Significant_figures
• False_precision

• noise; standard deviation; bandwith

• Discretization_error
• Nyquist–Shannon sampling theorem Aliasing Anti-aliasing Spatial_anti-aliasing Moiré_pattern

• Metrology