Approximating statistical functions by using fractional polynomial regression

Abstract

SUMMARY In statistics it is common to require a simple approximating equation for a smooth relationship between Yand X. The exact mathematical form may be known (but complicated) or unknown. We show that fractional polynomials are particularly good at providing concise and accurate formulae for representing such relationships. We give several examples, including the approximation of the 5% point of a statistic used in the analysis of means and of an unbiasing factor for calculating the standard deviation from a doubly censored normal sample.