Hotel Estoril Eden, Monte Estoril,
5-8 October 2005



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New Limiting Distribution for the Statistic Test for the Homogeneity of Two multinomial Populations

Adelaide Valente Freitas1, Miguel Pinheiro2, José Luís Oliveira2, Gabriela Moura3 and Manuel Santos3
1Departamento de Matemática, Universidade de Aveiro, Portugal
2IEETA, Universidade de Aveiro, Portugal
3Departamento de Biologia, Universidade de Aveiro, Portugal

Consider a sampled data cross-classified in a m x 2 contingency table from two populations described by a unknown multinomial probability distribution. For testing for the homogeneity of these two populations, Choulakian and Mahdi (2000) considered a statistic test (LD) defined by the maximum term of a random number of independent and identically distributed random variables. Applying Extreme Value Theory we derive a asymptotic probability distribution of the statistic LD, under convenient normalization, as m ® ¥. Simulation studies carried out show that for m large (m ³ 20) and for a large number of observations the empirical p-values are approximated quite accurately by the target p-values obtained using our limiting distribution.

Applying this approach on the complete ORFeome sequences of 3 yeast species, namely Saccharomyces cerevisiae, Saccharomyces mikatae and Schizosaccharomyces pombe for testing the homogeneity of some codon contexts of these species we conclude that the codon context rules for S. pombe are rather statistically significantly different from those rules of the other two species and similar for S. cerevisiae and S. mikatae. These results confirm the divergence and convergence of those three species in the phytogenetic tree.

Key Words and Phrases: extreme value distribution, random sample size, contingency table, ORFeome, phytogenetic tree

Choulakian, V. and Mahdi, S. (2001) A new statistic for the analysis of association between trait and polymorphic marker loci. Math. Biosciences, 164, 139-145.