Galton's midparent height revisited

Galton (Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246-263, 1886) defined midparent height as the average of the two parental heights. An alternative is to average the parental heights after converting them to standard deviation scores (SDSs). The aim of the paper is to compare the two midparent height calculations, and to see if they explain the imputation procedure used by Galton to adjust for the difference in adult height between daughters and sons. He multiplied daughters' heights by 1.08 before averaging them with sons' heights. Using data from 17 national height references it is shown that this procedure is equivalent to averaging the height SDSs of the sons and daughters. It demonstrates that midparent height SDS obtained by averaging the height SDSs of the two parents is a valid alternative to conventional midparent height.