Chi-square Reference Meanings: a Historical-epistemological Overview

Abstract

The present article shows a historical-epistemological study on the Chi-square statistic. In which theoretical-methodological notions from the Onto-Semiotic Approach (OSA) of mathematical cognition and instruction were used to identify four problems that have been key to the evolution of the Chi-square statistic: the Goodness-of-fit-test, the test of independence, the test of homogeneity and distribution. Furthermore, various meanings of the Chi-square statistic were recognized in the mathematical-statistical practices that are used to solve each of those problems. These meanings could help to establish epistemic criteria that allow, on the one hand, to propose progressive levels of inferential reasoning for the statistic (from informal to formal); and on the other hand, to design tasks oriented to promote the understanding of the diverse meanings of the Chi-square.