A cophenetic correlation coefficient for the modified Tocher's method

  • Anderson R Silva Professor Adjunto III Instituto de Ciências Exatas Universidade Federal de Alfenas
  • Carlos T. S. Dias
  • Paulo R. Cecon
  • Jaqueline A. Raminelli
  • Mário Puiatti


The cophenetic correlation coefficient has usually been taken as a measure of clustering consistence. However, its use has been restricted for hierarchical methods, at which is possible to obtain a cophenetic matrix. Nevertheless, Silva and Dias (2013) have proposed a simple algorithm to compute the cophenetic matrix for the original Tocher's method. Following the premise at which cophenetic values can be obtained even by ordination methods, the goal of this work is to extend that algorithm for computing the cophenetic matrix in cluster analysis performed via  modified Tocher's method and then to estimate the cophenetic correlation. To illustrate the procedure, we used two measure of distance: the squared generalized Mahalanobis and the Euclidean distance, based on six morphological characters of garlic cultivars. We performed comparisons of outcomes obtained with two hierarchical methods: Ward's algorithm and the average linkage. As expected, most of our results are according with those found by Silva and Dias (2013). The clustering consistence of agglomerative methods and the original and modified Tocher's can be evaluated by using a criterion in common, the correlation between original and cophenetic distances.

Biografia do Autor

Anderson R Silva, Professor Adjunto III Instituto de Ciências Exatas Universidade Federal de Alfenas
Doutor em Estatística e Experimentação Agropecuária com Pós-doutorado em Estatística Multivariada


CRUZ, C.D. Programa Genes: Biometria. Viçosa: Editora UFV, 2006. 382p.

R CORE TEAM. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. 2013. ISBN 3-900051-07-0, URL http://www.R-project.org/.

RAO, R.C. Advanced statistical methods in biometric research. New York: John Wiley and Sons, 1952. 390p.

SILVA, A.R. Métodos de agrupamento: avaliação e aplicação ao estudo de divergência genética em acessos de alho. 2012. 67p. Dissertação (Mestrado em Estatística Aplicada e Biometria), Universidade Federal de Viçosa, Viçosa, 2012.

SILVA, A.R. biotools: Tools for Biometry and Applied Statistics in Agricultural Science. R package version 1.1. 2014. URL http://CRAN.R-project.org/package=biotools.

SILVA, A.R.; DIAS, C.T.S. A cophenetic correlation coefficient for Tocher’s method. Pesquisa Agropecuária Brasileira, v.48, n.6, p.589-596, 2013.

SNEATH, P.H.A.; SOKAL, R.R. Numerical taxonomy: the principles and practice of numerical classification. San Francisco: W.H. Freeman and Company, 1973. 573p.

SOKAL, R.R.; ROHLF, F.J. The comparison of dendrograms by objective methods. Taxon, v.11, n.2, p.33-40, 1962.

VASCONCELOS, E.S.; CRUZ, C.D.; BHERING, L.L.; RESENDE JUNIOR, M.F.R. Método alternativo para analise´ de agrupamento. Pesquisa Agropecuária Brasileira, v.42, n.10, p.1421-1428, 2007.