Connecting Science and Mathematics: The Nature of Scientific and Statistical Hypothesis Testing

Abstract

Confusion persists concerning the roles played by scientific hypotheses and predictions in doing science. This confusion extends to the nature of scientific and statistical hypothesis testing. The present paper utilizes the If/and/then/Therefore pattern of hypothetico-deductive (HD) reasoning to explicate the nature of both scientific and statistical hypothesis testing. The central example is that of Gregor Mendel’s test his theory of inheritance and the use of the chi-square statistic to determine the extent to which his predicted and experimental results match. When the processes of scientific and statistical hypothesis testing are cast in HD terms, we find that both involve hypotheses, planned tests, predictions, results and conclusions. However, the former involves causal claims, while the latter is descriptive. Importantly, connecting the two processes reveals that scientific predictions and statistical hypotheses are the same thing. Improved understanding of the similarities and differences of the two processes and their connected role in doing science can be expected to improve general scientific and mathematical literacy. It may also improve the quality of research in science and mathematics education.