The use of transformation when comparing two means

摘要

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. 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 data to another scale where the assumption of normality is reasonable. The transformation which achieves a normal distribution should also give us similar variances. Table 2 shows the results of analyses using the square root, logarithmic, and reciprocal transformations. The log transformation gives the most similar variances and so gives the most valid test of significance. It also gives a reasonable approximation to a normal distribution.