Teaching statistical inference: a pedagogical critique of the assumption of known population variance

Abstract

This article critically analyzes the traditional teaching sequence for statistical inference, which introduces the assumption of known population variance as the starting point for estimating and testing hypotheses about the mean. From a pedagogical and epistemological perspective, it argues that this approach generates conceptual dissonance and hinders the development of authentic statistical reasoning by presenting as fundamental a scenario that rarely occurs in real-world research practice. Based on a critical analysis of the specialized literature and the coherence between teaching and professional practice, reflected in the use of statistical software packages that assume unknown variance by default, an alternative teaching approach is proposed. This approach begins instruction using the Student's t-distribution. A pedagogical sequence based on authentic problems is presented, designed to integrate sampling variability, standard error, and inferential uncertainty from early stages. It concludes that this approach fosters conceptual understanding and the transfer of knowledge to real-world research contexts.