A simple method for optimising transformation of non-parametric data: an illustration by reference to cortisol assays

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Neuroendocrine data are typically positively skewed and rarely conform to the expectations of a Gaussian distribution. This can be a problem when attempting to analyse results within the framework of the general linear model, which relies on assumptions that residuals in the data are normally distributed. One frequently used method for handling violations of this assumption is to transform variables to bring residuals into closer alignment with assumptions (as residuals are not directly manipulated). This is often attempted through ad hoc traditional transformations such as square root, log and inverse. However, Box and Cox (Box & Cox, 1964) observed that these are all special cases of power transformations and proposed a more flexible method of transformation for researchers to optimise alignment with assumptions. The goal of this paper is to demonstrate the benefits of the infinitely flexible Box–Cox transformation on neuroendocrine data using syntax in spss. When applied to positively skewed data typical of neuroendocrine data, the majority (˜2/3) of cases were brought into strict alignment with Gaussian distribution (i.e. a non-significant Shapiro–Wilks test). Those unable to meet this challenge showed substantial improvement in distributional properties. The biggest challenge was distributions with a high ratio of kurtosis to skewness. We discuss how these cases might be handled, and we highlight some of the broader issues associated with transformation. Copyright © 2016 John Wiley & Sons, Ltd.

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