Statistics Notes: The use of transformation when comparing two means

doi:10.1136/bmj.312.7039.1153

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J Martin Bland, professor of medical statisticsa,
Douglas G Altman, headb

^a Department of Public Health Sciences, St George's Hospital Medical School, London SW17 0RE
^b ICRF Medical Statistics Group, Centre for Statistics in Medicine, Institute of Health Sciences, PO Box 777, Oxford OX3 7LF

Correspondence to: Professor Bland.

The usual statistical technique used to compare the means of two groups is a confidence interval or significance test based on the t distribution. For this we must assume that the data are samples from normal distributions with the same variance. Table 1 shows the biceps skinfold measurements for 20 patients with Crohn's disease and nine patients with coeliac disease.

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Table 1

Biceps skinfold thickness (mm) in two groups of patients

The data have been put into order of magnitude, and it is fairly obvious that the distribution is skewed and far from normal. When, as here, the assumption of normality is wrong we can often transform the …