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Better Articulating Normal Curve Theory for Introductory Mathematical Statistics Students: Power Transformations and Their Back-Transformations

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  • Daniel A. Griffith

Abstract

This article addresses a gap in many, if not all, introductory mathematical statistics textbooks, namely, transforming a random variable so that it better mimics a normal distribution. Virtually all such textbooks treat the subject of variable transformations, which furnishes a nice opportunity to introduce and study this transformation-to-normality topic, a topic students frequently encounter in subsequent applied statistics courses. Accordingly, this article reviews variable power transformations of the Box--Cox type within the context of normal curve theory, as well as addresses their corresponding back-transformations. It presents four theorems and a conjecture that furnish the basics needed to derive equivalent results for all nonnegative values of the Box--Cox power transformation exponent. Results are illustrated with the exponential random variable. This article also includes selected pedagogic tools created with R code.

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  • Daniel A. Griffith, 2013. "Better Articulating Normal Curve Theory for Introductory Mathematical Statistics Students: Power Transformations and Their Back-Transformations," The American Statistician, Taylor & Francis Journals, vol. 67(3), pages 157-169, August.
    • Handle: RePEc:taf:amstat:v:67:y:2013:i:3:p:157-169
    DOI: 10.1080/00031305.2013.801782
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    Cited by:

    1. Daniel A. Griffith, 2014. "Reply," The American Statistician, Taylor & Francis Journals, vol. 68(1), pages 67-69, February.
    2. Daniel A. Griffith & Yongwan Chun, 2021. "Soil Sample Assay Uncertainty and the Geographic Distribution of Contaminants: Error Impacts on Syracuse Trace Metal Soil Loading Analysis Results," IJERPH, MDPI, vol. 18(10), pages 1-28, May.
    3. Daniel A. Griffith, 2022. "Reciprocal Data Transformations and Their Back-Transforms," Stats, MDPI, vol. 5(3), pages 1-24, July.
    4. Daniel A. Griffith, 2019. "Negative Spatial Autocorrelation: One of the Most Neglected Concepts in Spatial Statistics," Stats, MDPI, vol. 2(3), pages 1-28, August.

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