Positively skewed data: revisiting the Box-Cox power transformation

Jake Olivier, Melissa M. Norberg

Research output: Contribution to journalArticlepeer-review


Although the normal probability distribution is the cornerstone of applying statistical methodology; data do not always meet the necessary normal distribution assumptions. In these cases, researchers often transform non normal data to a distribution that is approximately normal. Power transformations constitute a family of transformations, which include logarithmic and fractional exponent transforms. The Box-Cox method offers a simple method for choosing the most appropriate power transformation. Another option for data that is positively skewed, often used when measuring reaction times, is the Ex-Gaussian distribution which is a combination of the exponential and normal distributions. In this paper, the Box-Cox power transformation and Ex-Gaussian distribution will be discussed and compared in the context of positively skewed data. This discussion will demonstrate that the Box-Cox power transformation is simpler to apply and easier to interpret than the Ex-Gaussian distribution.
Original languageEnglish
Pages (from-to)68-75
Number of pages8
JournalInternational Journal of Psychological Research
Issue number1
Publication statusPublished - 2010
Externally publishedYes


  • Logarithmic transformations
  • geometric mean analysis
  • ex-Gaussian distribution
  • log-normal distribution


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