History of Science and Statistical Education

History of Science and Statistical Education: Examples from Fisherian and Pearsonian schools Paper presented at the 2004 Joint Statistical Meeting, Toronto, Canada Chong Ho Yu, Ph.D. [email protected] website: http://www.creative-wisdom/pub/pub.html Abstract Many students share a popular misconception that statistics is a subject-free methodology derived from invariant and timeless mathematical axioms. It is proposed that statistical education should include the aspect of history/philosophy of science. This article will discuss how statistical methods developed by Karl Pearson and R. A. Fisher are driven by biological themes and philosophical presumptions. Pearson was pre-occupied with between-group speciation and thus his statistical methods, such as the Chi-squared test, are categorical in nature. On the other hand, variation within species plays a central role in Fisher’s framework, and therefore, Fisher’s approach, such as partitioning variance, is concerned with interval-scaled data. In addition, Fisher adopted a philosophy of embracing causal inferences and theoretical entities, such as infinite population and gene, while Pearson disregarded unobservable and insisted upon description of the data at hand. These differences lead to the subsequent divergence of two hypothesis testing methods, developed by R. A. Fisher and Neyman/E .S. Pearson, son of Karl Pearson, respectively. Students will appreciate the meanings of Fisherian and Pearsonian methods if they are exposed to history and philosophy of science.