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Education And Debate

Statistics Notes: Transforming data

BMJ 1996; 312 doi: (Published 23 March 1996) Cite this as: BMJ 1996;312:770
  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.

    We often transform data by taking the logarithm, square root, reciprocal, or some other function of the data. We then analyse the transformed data rather than the untransformed or raw data. We do this because many statistical techniques, such as t tests, regression, and analysis of variance, require that data follow a distribution of a particular kind. The observations themselves must come from a population which follows a normal distribution,1 and different groups of observations must come from populations which have the same variance or standard deviation. We need this uniform variance because we estimate the variance within the groups, and we can do this well only if we can assume it to be the same in each group. Many biological variables do follow a normal distribution with uniform variance. Many of those which do not can be made to do so by a suitable transformation. Fortunately, a transformation which makes data follow a normal distribution …

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