Used to assess the goodness of fit between the model and observed cosmic-ray spectra.The chi-squared test is a statistical method that measures how well an observed distribution matches an expected theoretical distribution. In physics, it is commonly used to evaluate the goodness of fit between experimental data and model predictions, such as comparing measured cosmic-ray spectra with theoretical models. The test quantifies the discrepancy by summing the squared differences between observed and expected values, each normalized by the expected variance.
Developed by Karl Pearson in 1900 as a goodness-of-fit test, originally for analyzing categorical data in biology and later adopted across physics and other sciences.
For each data point, compute (observed − expected)² / expected, then sum these values to get the chi-squared statistic. A smaller value indicates a better fit. The statistic follows a chi-squared distribution with degrees of freedom equal to the number of data points minus the number of fitted parameters. A p-value can then be derived to assess whether the deviation is statistically significant or just due to random fluctuations.
Widely used in experimental physics for model validation, including cosmic-ray spectrum analysis, particle physics cross-section measurements, and detector calibration.
The chi-squared test is so fundamental that it appears in the discovery of the Higgs boson, where physicists used it to confirm that the observed data matched the Standard Model prediction within statistical uncertainties.
