Positively skewed data: revisiting the box-cox power transformation.
Jake Olivier
University of New South Wales
Melissa M. Norberg
University of New South Wales


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

How to Cite

Olivier, J., & M. Norberg, M. (2010). Positively skewed data: revisiting the box-cox power transformation. International Journal of Psychological Research, 3(1), 68-77. https://doi.org/10.21500/20112084.846


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.


Box, G.E.P., & Cox, D. R. (1964).An analysis of transformations.Journal of the Royal Statistical Society, Series B, 26, 211–252.

Brown, J. D. (1997). Statistics corner: Questions and answers about language testing statistics: Skewness and kurtosis. Shiken, 1, 20-23. Available online at www.jalt.org/test/bro_1.htm. [16 Aug. 1997].

Conover, W.J. (1998). Practical Nonparametric Statistics. Hoboken, NJ: Wiley.

Heathcote, A. (1996). RTSYS: A DOS application for the analysis of reaction time data. Behavior Research Methods, Instruments, and Computers, 28, 427-445.

Heeren, T. &D’Agostino R. (1987). Robustness of the two independent samples t-test when applied to ordinal scaled data. Statistics in Medicine, 6, 79-90.

Olivier, J., Johnson, W.D., Marshall, G.D. (2008). The logarithmic transformation and the geometric mean in reporting experimental IgE results: What are they and when and why to use them?Annals of Allergy, Asthma and Immunology, 100, 333-337. Erratum in: Annals of Allergy, Asthma and Immunology, 100, 625-626.

SAS Institute Inc. (2008). SAS/STAT® 9.2 User’s Guide. Cary, NC: SAS Institute Inc.

Wackerly, D., Mendenhall W., and Scheaffer R. (2007).Mathematical Statistics with Applications, 7thEdition.Belmont, CA: Duxbury.

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The work that is sent to this journal must be original, not published or sent to be published elsewhere; and if it is accepted for publication, authors will agree to transfer copyright to International Journal of Psychological Research. 

To give up copyright, the authors allow that, International Journal of Psychological Research, distribute the work more broadly, check for the reuse by others and take care of the necessary procedures for the registration and administration of copyright; at the same time, our editorial board represents the interests of the author and allows authors to re-use his work in various forms. In response to the above, authors transfer copyright to the journal, International Journal of Psychological Research. This transfer does not imply other rights which are not those of authorship (for example those that concern about patents). Likewise, preserves the authors rights to use the work integral or partially in lectures, books and courses, as well as make copies for educational purposes. Finally, the authors may use freely the tables and figures in its future work, wherever make explicit reference to the previous publication in International Journal of Psychological Research. The assignment of copyright includes both virtual rights and forms of the article to allow the editorial to disseminate the work in the manner which it deems appropriate. 

The editorial board reserves the right of amendments deemed necessary in the application of the rules of publication.