Two-stage transformation systems for normalization of reference distributions evaluated.

In two-stage transformation systems for normalization of reference distributions, the asymmetry is first corrected, and any deviation of kurtosis is then adjusted. The simulation studies reported here show that these systems have previously been assessed too optimistically because the sample variation of the transformation parameters was neglected. Applying a goodness-of-fit test to transformed values shows that one should accept gaussianity only for p-values greater than 0.15 instead of those greater than 0.05. Further, the calculated 90% confidence intervals of reference limits should be expanded by 25%. When the correct level of significance is used, only real reference distributions that deviate moderately from the gaussian form are normalized. Calculation of confidence intervals demonstrated that 50 to 450 subjects are needed for a precise parametric estimation of the 95% reference interval. For the nonparametric approach, 125 to 700 reference subjects are necessary. The larger sample sizes are needed when distributions show pronounced skewness.