An approach to the estimation of growth standards: the univariate case

This paper shows how reference values can be determined when the underlying characteristic (say, weight) follows a distribution that is not too distant from the Gaussian. Application of the normalizing Box-Cox power transformation is the basis of our approach. This transformation is monotonic and hence invertible, so offering the choice of two scales of measurement on which to work--the original and the Gaussian. Modified versions of the procedure are provided allowing use of the basic transformation in the presence of certain deficiencies in the data, principally measurement error and misclassification. It is shown that application of Box-Cox to a cohort at several points in time can be quite revealing. When the data are already symmetrical the Box-Cox transformation has no effect: in this case the John-Draper modulus transformation and modifications of it are shown to be helpful. All of this is illustrated by using data from the Swedish Longitudinal Growth Study.