Conceptual issues in understanding the inner logic of statistical inference: Insights from two teaching experiments

•Students explored connections among ideas of sampling distributions and statistical inference.•Students often understood individual ideas of sample, population, and sampling distributions.•Yet, students had difficulty composing the individual ideas into a coherent scheme for inference.•Composing the ideas into a coherent scheme is a key challenge in understanding inference deeply.

We report on a sequence of two classroom teaching experiments that investigated high school students’ understandings as they explored connections among the ideas comprising the inner logic of statistical inference—ideas involving a core image of sampling as a repeatable process, and the organization of its outcomes into a distribution of sample statistics as a basis for making inferences. Students’ responses to post-instruction test questions indicate that despite understanding various individual components of inference—a sample, a population, and a distribution of a sample statistic—their abilities to coordinate and compose these into a coherent and well-connected scheme of ideas were usually tenuous. We argue that the coordination and composition required to assemble these component ideas into a coherent scheme is a major source of difficulty in developing a deep understanding of inference.