Notes on the statistics of growth standards

Abstract

The problems of constructing population standards for measurements such as height and age points such as menarche are discussed. Extreme centiles, such as the 3rd, estimated from a Gaussian distribution have a considerable imprecision, the amount of which is detailed. Non-parametric estimation, as usually used for weight, is compared with transformation to Gaussianity and thence parametric estimation. Regression standards are discussed, whereby the subject is compared with a relevant subsection of the population rather than all of it, and it is suggested that velocity of growth standards might be couched in these terms.