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 b y the US Bureau of the Census in 1990 are homogeneous-a hypothesis we rejec t. Rather, we find that US central cities consist of 2 distinct subsets of municipalities that are aggregated from 13 cluster groupings. The article h as two purposes. The first is methodological. We develop a method that uses cluster analysis to group US central cities; then we employ discriminant a nalysis to establish the statistical validity of those groups. We also deve lop techniques to minimise the role of judgement in selecting the appropria te cluster solution. The second purpose of the article is to test the subst antive null hypothesis. Our rejection of the homogeneity assumption raises the spectre of specification error in research and public policies that ass ume homogeneity among central cities.