Education and debate

Statistics Notes: The use of transformation when comparing two means

^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.

Table 1--Biceps skinfold thickness (mm) in two groups of
patients
----------------------------------------------------------
          Crohn's disease              Coeliac disease
----------------------------------------------------------
   1.8     2.8       4.2    6.2        1.8         3.8
   2.2     3.2       4.4    6.6        2.0         4.2
   2.4     3.6       4.8    7.0        2.0         5.4
   2.5     3.8       5.6   10.0        2.0         7.6
   2.8     4.0       6.0   10.4        3.0
----------------------------------------------------------
            Mean=4.72                    Mean=3.53
             SD=2.42                      SD=1.96

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 . . . [Full text of this article]

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