WITHDRAWN: Asymptotic Distribution of Similarity Coefficients and Similarity Tests

• Author(s): Hanzhe Zheng and Larry P. Ammann
• Keywords: similarity coefficients ; similarity tests ; random allocation theories ; large sample theories

Abstract

Quantitative measures of similarity or resemblance between samples (such as biological communities) play an important role in many areas such as genetic, ecological and environmental studies. We introduce a new overall similarity coefficient of p samples which can measure the overall degree of association of these p samples and will reduce to the usual pairwise similarity coefficient when p = 2. Using the random allocation theories and large sample theories, we establish the asymptotic distributions of both overall and pairwise similarity coefficients. Also we propose two types of similarity tests to test the degree of association of these p samples and apply simulation to study the power of these two types of tests. In addition, we perform some similarity tests based on the simulated data sets.