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Abstract
Teaching undergraduate statistics has long been dominated by a parallel ap- proach, where large and small sample inference is taught side-by-side. Necessarily, the set of assumptions for the two cases is different, with normality and homoskedas- ticity being the main ingredients for the popular t- and F-tests in small samples. This paper advocates a change of paradigm and the exclusive presentation of large sample inference in introductory classes, for three reasons: First, it weakens and simplifies the assumptions. Second, it reduces the number of sampling distributions and therefore simplifies the presentation. Third, it may give better performance in many small sample situations where the assumptions such as normality are violated. The detection of these violations in small samples is inherently difficult due to low power of normality or homoskedasticity tests. Many numerical examples are given. In the era of big data, it is anachronistic to deal with small sample inference in introductory statistics classes, and this paper makes the case for a change.
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Hafner, C. (2021). Teaching statistical inference without normality (LIDAM Discussion Paper ISBA 2021/27). https://hdl.handle.net/2078.5/110577