Article

The log transformation is special

Department of Medical Statistics, Glaxo Research and Development Ltd., Greenford, Middlesex, U.K.
Statistics in Medicine (Impact Factor: 1.83). 04/1995; 14(8):811-9. DOI: 10.1002/sim.4780140810
Source: PubMed

ABSTRACT

The logarithmic (log) transformation is a simple yet controversial step in the analysis of positive continuous data measured on an interval scale. Situations where a log transformation is indicated will be reviewed. This paper contends that the log transformation should not be classed with other transformations as it has particular advantages. Problems with using the data themselves to decide whether or not to transform will be discussed. It is recommended that log transformed analyses should frequently be preferred to untransformed analyses and that careful consideration should be given to use of a log transformation at the protocol design stage.

    • "Moreover, the interpretation of hormone ratios is complicated and in many cases not sufficiently supported from a theoretical point of view. By contrast , the statistical properties of ratios, their interpretation, and associated problems have been controversially discussed for several decades in other disciplines such as finance and accounting (e.g., Bedingfield et al., 1985; Deakin, 1976; Frecka and Hopwood, 1983; Kane and Meade, 1998), biology (e.g., Atchley et al., 1976), medicine (e.g., Gullberg, 1991; Keene, 1995; Senn, 1989), and geology (e.g., Chayes, 1949; Weltje, 2012). These established insights will be considered and incorporated throughout the course of this article. "
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    ABSTRACT: Hormone ratios have become increasingly popular throughout the neuroendocrine literature since they offer a straightforward way to simultaneously analyze the effects of two interdependent hormones. However, the analysis of ratios is associated with statistical and interpretational concerns which have not been sufficiently considered in the context of endocrine research. The aim of this article, therefore, is to demonstrate and discuss these issues, and to suggest suitable ways to address them. In a first step, we use exemplary testosterone and cortisol data to illustrate that one major concern of ratios lies in their distribution and inherent asymmetry. As a consequence, results of parametric statistical analyses are affected by the ultimately arbitrary decision of which way around the ratio is computed (i.e., A/B or B/A). We suggest the use of non-parametric methods as well as the log-transformation of hormone ratios as appropriate methods to deal with these statistical problems. However, in a second step, we also discuss the complicated interpretation of ratios, and propose moderation analysis as an alternative and oftentimes more insightful approach to ratio analysis. In conclusion, we suggest that researchers carefully consider which statistical approach is best suited to investigate reciprocal hormone effects. With regard to the hormone ratio method, further research is needed to specify what exactly this index reflects on the biological level and in which cases it is a meaningful variable to analyze.
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    • "In particular , the residuals from the accuracy data , which typically exhibit a skewed distribution , were in our case satisfactorily normal , allowing us to use simple parametric tests . When necessary , log - transformation ( Keene , 1995 ) was used on non - normally distributed data . "
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    • "n/N control; n/N HF). Continuous scale data was log 10 transformed [38] and differences between control and HF animals determined using linear mixed modelling to account for instances where multiple cellular observations (n) were obtained from each experimental subject (N) (IBM SPSS Statistics v20). Where treatments/effects were within the same animal, cellular differences were assessed using a paired Students t-test and considered significant when P b 0.05. "
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