Chivelle: Chi-Squared Goodness of Fit
Measurement, Noise & the Lab arc, page 130 of 193. Back to The Pixelated Physics Universe
Who they are
Chivelle has one line, and says it often: “Chi²/ndf = 0.2. reviewer 2 is suspicious.”
Chivelle 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
χ² per degree of freedom near 1 indicates a good fit; much less than 1 means the error bars were overestimated.
$$ \begin{gathered} \frac{\chi^{2}}{\nu} \approx 1 \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\chi^{2}$ | chi-squared of the fit | — |
| $\nu$ | number of degrees of freedom | — |
Sources
- Particle Data Group, 'Statistics' review (2022), goodness-of-fit section
Crossovers
Chivelle meets Nullwen (Upper Limit Statistics). Nullwen turns a non-detection into a precise upper limit. Chivelle checks that the fit behind it is honest: a χ²/ndf far below 1 means the error bars were inflated.
Chivelle meets Quadrell (Error Propagation). Chivelle's χ² depends on honest error bars. Quadrell builds them: independent uncertainties add in quadrature, and correlated ones do not.
Wear the lore
Concept keywords: Chi-Squared Goodness of Fit, Chivelle, Measurement, Noise & the Lab, physics lore, Pixelated Physics