Analogies and differences between the logic behind statistical hypothesis testing and proofs by contradiction: What can we learn from them?

Statistical Hypothesis Testing (SHT) is widely employed across numerous scientific disciplines, and a clear understanding of its underlying logic is essential for the broader scientific community. Here, drawing upon both epistemological and statistical perspectives, we aim to clarify—primarily for educational purposes—the logical relationship between Proof by Contradiction (PBC) and SHT. We begin by outlining the logics of SHT and PBC, followed by a discussion of their key similarities and differences. We then explore the pedagogical value of these analogies and distinctions through illustrative examples. Our objective is to help prevent common misinterpretations in the application of SHT, particularly in the interpretation of its outcomes. By elucidating the conceptual parallels between SHT and PBC, we aim to make the logical structure of SHT more transparent. Finally, we highlight and discuss several critical aspects relevant to teaching, with the intention of enhancing the pedagogical effectiveness of instruction in this area.