Power and robustness of Aitchison's test for complete subcompositional independence in closed arrays |
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| Authors: | Alex Woronow |
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| Institution: | (1) Geosciences Department, University of Houston, UP, 77004 Houston, Texas |
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| Abstract: | This paper examines some aspects of the power and robustness of the test for complete subcompositional independence proposed by Aitchison (1982). Although the computed test statistics commonly do not approach being  2 distributed throughout their range, the upper tail of their distribution does mimic the 2 distribution sufficiently to yield a quite robust test when variates are drawn from identical distributions with different distribution parameters or even when variates are drawn from different distributions. But the magnitude of correlations among the variables and the proportion of correlated to independent variables that compose the closed data vectors affect the power of the test. |
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| Keywords: | closed number systems closure log ratio compositional data logistic-normal distribution correlations among proportions |
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