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