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Robust permutation tests for homogeneity of fingerprint patterns of dioxin congener profiles

Fingerprint analysis comparing the polychlorinated dibenzo‐p‐dioxin and dibenzofuran (PCDD/F) congener profile patterns of collected samples with those of potential dioxin emission source(s) is an important tool for identifying environmental dioxin pollution. The constraint that the proportions of the 17 PCDD/F congeners comprising a fingerprint sum up to one motivates a multivariate gamma distribution, which leads to a Dirichlet distribution. Because of the complexity in restricted likelihood ratio tests and typical sample size limitations resulting from laboratory analysis costs, permutation test procedures are employed for hypothesis testing of the homogeneity of congener profiles. Pearson‐type chi‐squared tests based on the Dirichlet distribution (DM) assumption, the generalized form of DM using the arithmetic mean and geometric mean of the proportions, and the robust aligned rank test, are proposed and compared through simulations. PCDD/F samples collected from the stack of a local municipal solid waste incinerator and from ambient air near the municipal solid waste incinerator in Taiwan were illustrated as an example. The simulation results showed that the aligned rank test, followed by the DM‐based test, was generally robust to distributional assumptions and had high statistical power. The arithmetic‐mean‐based and geometric‐mean‐based tests outperformed one another in different conditions, dependent on the underlying distribution. Copyright © 2012 John Wiley & Sons, Ltd.