Testing for normality in truncated anthropometric samples - Antonio Fidalgo (European Historical Economics Society (EHES), 2018)
Anthropometric historical analysis depends on the assumption that human characteristics—such as height—are normally distributed. I propose and evaluate a metric entropy, based on nonparametrically estimated densities, as a statistic for a consistent test of normality. My first test applies to full distributions for which other tests already exist and performs similarly. A modified version applies to truncated samples for which no test has been previously devised. This second test exhibits correct size and high power against standard alternatives. In contrast to the distributional prior of Floud et al. (1990), the test rejects normality in large parts of their sample; the remaining data reveal a downward trend in height, not upward as they argue.
Keywords: C12; C14; N3; N13; J11; 330; test of normality; truncated samples; anthropometrics