On the Pearson-Fisher chi-squared theorem
Aniello Buonocore, Enrica Pirozzi · Applied Mathematical Sciences · 2014
This paper outlines with modern notations the proof of Karl Pearson on the distribution of the statistic on which the chi-squared goodness of t test with simple null hypothesis is based. It is then shown in details a proof due Ronald Aylmer Fisher, which in the opinion of the authors has not received the proper attention for its elegance and its immediate generalization to the case of composite null hypothesis. Finally, a new proof based on the Principle of mathematical induction is provided by making use of widely known probabilistic results. Mathematics Subject Classication: 62-02; 62F03; 62G10