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Pearson, K. (1900) On the Criterion that a Given System of Deviations from the Probable in the Case of Correlated System of Variables Is Such That It Can Be Reasonably Supposed to Have Arisen from Random Sampling. Philosophical Magazine Series 5, 50, 157-175.
https://doi.org/10.1080/14786440009463897

has been cited by the following article:

• TITLE: Chi-Square Distribution: New Derivations and Environmental Application

  AUTHORS: Thomas M. Semkow, Nicole Freeman, Umme-Farzana Syed, Douglas K. Haines, Abdul Bari, Abdul J. Khan, Kimi Nishikawa, Adil Khan, Adam G. Burn, Xin Li, Liang T. Chu

  KEYWORDS: Mathematical Induction, Laplace Transform, Gamma Distribution, Chi-Square Test, Gross Alpha-Beta, Drinking Water

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.7 No.8, August 19, 2019

  ABSTRACT: We describe two new derivations of the chi-square distribution. The first derivation uses the induction method, which requires only a single integral to calculate. The second derivation uses the Laplace transform and requires minimum assumptions. The new derivations are compared with the established derivations, such as by convolution, moment generating function, and Bayesian inference. The chi-square testing has seen many applications to physics and other fields. We describe a unique version of the chi-square test where both the variance and location are tested, which is then applied to environmental data. The chi-square test is used to make a judgment whether a laboratory method is capable of detection of gross alpha and beta radioactivity in drinking water for regulatory monitoring to protect health of population. A case of a failure of the chi-square test and its amelioration are described. The chi-square test is compared to and supplemented by the t-test.