Introduction

Human growth has always fascinated statisticians, judging by the number of statistics books that use weight or height data for examples. The fascination may be due not only to the ready availability and statistically well-behaved nature of the data, but also to the fact that growth is universal: everybody has experienced it.

The most obvious statistical construct used in this study of human growth is the fiction that growth is a smooth process. Recent work on knemometry (Hermanussen et al., 1988) has shown that on a sufficiently short time scale the process is anything but smooth, proceeding in fits and starts over periods of weeks. Equally, on a scale of months there are important seasonal influences on growth. This is particularly so in the Third World, where growth rates can vary enormously from one season to another, but even in the Western world there is clear evidence of seasonally (Marshall, 1971).

If height is measured annually, these oscillations ought to cancel out and give an impression of smooth progress. In practice, annual height velocities are far from smooth when plotted, so that even on this time scale growth is discontinuous. Despite this, it has been found useful over the years to retain the concept of smoothness in growth, on the grounds that when averaged over large samples, the oscillations do cancel out. This is particularly relevant for constructing growth charts.

Growth charts provide a simple and convenient means of displaying serial growth data in individual subjects. A growth chart consists of several smooth curves, usually seven, showing how centiles of the distribution of the chosen measurement change with age.