Explorations in statistics: the log transformation

Advances in Physiology Education
Douglas Curran-Everett

Abstract

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This thirteenth installment of Explorations in Statistics explores the log transformation, an established technique that rescales the actual observations from an experiment so that the assumptions of some statistical analysis are better met. A general assumption in statistics is that the variability of some response Y is homogeneous across groups or across some predictor variable X. If the variability-the standard deviation-varies in rough proportion to the mean value of Y, a log transformation can equalize the standard deviations. Moreover, if the actual observations from an experiment conform to a skewed distribution, then a log transformation can make the theoretical distribution of the sample mean more consistent with a normal distribution. This is important: the results of a one-sample t test are meaningful only if the theoretical distribution of the sample mean is roughly normal. If we log-transform our observations, then we want to confirm the transformation was useful. We can do this if we use the Box-Cox method, if we bootstrap the sample mean and the statistic t itself, and if we assess the resi...Continue Reading

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Jul 27, 2017·Advances in Physiology Education·Douglas Curran-Everett

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Citations

Jun 25, 2020·Journal of Clinical Medicine·Ya-Ting HuangChih-Chung Shiao
Aug 1, 2020·International Journal of Molecular Sciences·Gabriella DobraKrisztina Buzas
Oct 15, 2019·Temperature : Multidisciplinary Biomedical Journal·Aaron R Caldwell, Samuel N Cheuvront
Mar 17, 2021·American Journal of Community Psychology·Elaina R McWilliams, Bronwyn A Hunter
May 19, 2021·Medical Image Analysis·Lu ZhangUNKNOWN Alzheimer’s Disease Neuroimaging Initiative
Sep 15, 2021·Movement Disorders : Official Journal of the Movement Disorder Society·Linliu PengHong Jiang
Aug 19, 2021·Bioinformatics·Llambrich MariaCumeras Raquel
Nov 24, 2020·Value in Health Regional Issues·Agner Pereira LanaMariângela Leal Cherchiglia

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