What is a central city in the United States? Applying a statistical technique for developing taxonomies

We test the null hypothesis that municipalities defined as central cities by the US Bureau of the Census in 1990 are homogeneous-a hypothesis we reject. Rather, we find that US central cities consist of 2 distinct subsets of municipalities that are aggregated from 13 cluster groupings. The article has two purposes. The first is methodological. We develop a method that uses cluster analysis to group US central cities; then we employ discriminant analysis to establish the statistical validity of those groups. We also develop techniques to minimise the role of judgement in selecting the appropriate cluster solution. The second purpose of the article is to test the substantive null hypothesis. Our rejection of the homogeneity assumption raises the spectre of specification error in research and public policies that assume homogeneity among central cities.