Journal of Classification

, Volume 2, Issue 1, pp 77–108 | Cite as

On some significance tests in cluster analysis

  • H. H. Bock
Authors Of Articles

Abstract

We investigate the properties of several significance tests for distinguishing between the hypothesisH of a “homogeneous” population and an alternativeA involving “clustering” or “heterogeneity,” with emphasis on the case of multidimensional observationsx1, ...,x n ε p . Four types of test statistics are considered: the (s-th) largest gap between observations, their mean distance (or similarity), the minimum within-cluster sum of squares resulting from a k-means algorithm, and the resulting maximum F statistic. The asymptotic distributions underH are given forn→∞ and the asymptotic power of the tests is derived for neighboring alternatives.

Keywords

Significance test Homogeneity Heterogeneity Gap test Minimum within-cluster sum of squares Maximum F statistics Asymptotic normal distribution 

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Copyright information

© Springer-Verlag New York Inc 1985

Authors and Affiliations

  • H. H. Bock
    • 1
  1. 1.Institut für Statistik und WirtschaftsmathematikTechnical University AachenAachenWest Germany

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