On the construction of cross-sectional statistical standards for growth

Cross-sectional growth studies generally produce standardizing groups which are too small to permit the direct construction of standards. This problem can be circumvented by the introduction of appropriate structural assumptions. The two key papers in the literature which focus on this issue, Healy (1962) and Goldstein (1972), give methodologies which involve somewhat different premises. Healy takes the ages of individuals to be uniformly distributed over a well-defined interval (but their precise levels unknown). Goldstein by comparison supposes age levels to be known exactly. Both authors postulate that the characteristic of interest follows a Gaussian density whose mean and variance are each linear functions of time, a + bt and c + dt, say. In this paper we begin to explore the robustness of the two methods. Our results show that Healy's original moment solution to the estimation of (a, b, c and d) may be quite insensitive to departures from a uniform distribution for ages provided that this distribution remains symmetric about the interval mid-point. Moreover, the distribution of the characteristic of interest may deviate from the Gaussian without too much effect, provided that symmetry about the mean a + bt is retained. However, there is much more doubt about asymmetric departures in both cases especially with regard to the estimation of b and d. Opting for simple 'interpolated' estimates of these two parameters (when possible) rather than Healy's original formula-based versions will strongly aid robustness in general.(ABSTRACT TRUNCATED AT 250 WORDS)