Quadrell: Error Propagation
Measurement, Noise & the Lab arc, page 131 of 193. Back to The Pixelated Physics Universe
Who they are
Quadrell has one line, and says it often: “Errors add in quadrature. problems don't.”
Quadrell is a character of the Measurement, Noise & the Lab arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Independent uncertainties combine in quadrature: σ² = Σ (∂f/∂xi)² σi². Correlated ones do not.
$$ \begin{gathered} \sigma^{2} = \sum_i \left(\frac{\partial f}{\partial x_i}\right)^{2} \sigma_i^{2} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\sigma$ | combined standard uncertainty of f | — |
| $f$ | measured function | — |
| $x_i$ | input quantity | — |
| $\sigma_i$ | standard uncertainty of x_i | — |
Sources
- JCGM 100:2008 (GUM), §5.1 and §5.2, BIPM
Crossovers
Quadrell meets Chivelle (Chi-Squared Goodness of Fit). Chivelle's χ² depends on honest error bars. Quadrell builds them: independent uncertainties add in quadrature, and correlated ones do not.
Quadrell meets Radicane (Poisson Counting Statistics). Radicane's counting error is √N. Quadrell combines it with every other independent uncertainty by adding the squares.
Wear the lore
Concept keywords: Error Propagation, Quadrell, Measurement, Noise & the Lab, physics lore, Pixelated Physics