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Teaching statistical inference without normality

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  • Hafner, Christian

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

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.

Suggested Citation

  • Hafner, Christian, 2021. "Teaching statistical inference without normality," LIDAM Discussion Papers ISBA 2021027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2021027
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    References listed on IDEAS

    as
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    2. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    3. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
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    Keywords

    sampling distributions ; simplification ; big data;
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