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Statistics notes: Transformations, means, and confidence intervals

BMJ 1996; 312 doi: https://doi.org/10.1136/bmj.312.7038.1079 (Published 27 April 1996) Cite this as: BMJ 1996;312:1079
  1. J Martin Bland, professor of medical statisticsa,
  2. Douglas G Altman, headb
  1. a Department of Public Health Sciences, St George's Hospital Medical School, London SW17 0RE
  2. b ICRF Medical Statistics Group, Centre for Statistics in Medicine, Institute of Health Sciences, PO Box 777, Oxford OX3 7LF
  1. Correspondence to: Professor Bland.

    When we use transformed data in analyses,1 this affects the final estimates that we obtain. Figure 1 shows some serum triglyceride measurements, which have a skewed distribution. A logarithmic transformation is often useful for data which have positive skewness like this, and here the approximation to a normal distribution is greatly improved. For the untransformed data the mean is 0.51 mmol/l and the standard deviation 0.22 mmol/l. The mean of the log10 transformed data is -0.33 and the standard deviation is 0.17. If we take the mean on the transformed scale and back transform by taking the antilog, we get …

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