Origin of the correlation coefficient and its multifaceted interpretation

Abstract

Pearson’s correlation coefficient is an important statistic. For over a century, the index has been used in various branches of science. This paper introduces both its creation and initial developments that are often forgotten or ignored. Because no theory is independent of the original setting and the research plan of its creators, knowledge about the context of pioneering ideas helps researchers better understand the meaning of the coefficient. The paper highlights the work of Bravais, Galton, Pearson, artillery scientists, Spearman, and many other early contributors, and describes their original intentions, achievements, and faults. Key comments on the present statistical theories and practices are also presented in several pivotal comments.