Open AccessWhy is it difficult to understand statistical inference? Reflections on the opposing directions of construction and application of inference framework
Author(s) -
Fulya Kula,
Rüya Gökhan Koçer
Publication year - 2020
Publication title -
teaching mathematics and its applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.452
H-Index - 18
eISSN - 1471-6976
pISSN - 0268-3679
DOI - 10.1093/teamat/hrz014
Subject(s) - inference , statistical inference , sampling distribution , fiducial inference , computer science , statistical theory , sample (material) , population , artificial intelligence , sampling (signal processing) , machine learning , statistical hypothesis testing , theoretical computer science , frequentist inference , mathematics , statistics , bayesian inference , sociology , bayesian probability , chemistry , demography , filter (signal processing) , chromatography , computer vision
Difficulties in learning (and thus teaching) statistical inference are well reported in the literature. We argue the problem emanates not only from the way in which statistical inference is taught but also from what exactly is taught as statistical inference. What makes statistical inference difficult to understand is that it contains two logics that operate in opposite directions. There is a certain logic in the construction of the inference framework, and there is another in its application. The logic of construction commences from the population, reaches the sample through some steps and then comes back to the population by building and using the sampling distribution. The logic of application, on the other hand, starts from the sample and reaches the population by making use of the sampling distribution. The main problem in teaching statistical inference in our view is that students are taught the logic of application while the fundamental steps in the direction of construction are often overlooked. In this study, we examine and compare these two logics and argue that introductory statistical courses would benefit from using the direction of construction, which ensures that students internalize the way in which inference framework makes sense, rather than that of application.