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Title: Functional experimental design via analytic permutation testing Authors:  Adam Kashlak - University of Alberta (Canada) [presenting]
Sergii Myroshnychenko - University of Alberta (Canada)
Susanna Spektor - The Sheridan College Institute of Technology and Advanced Learning (Canada)
Abstract: Permutation testing is a powerful non-parametric testing procedure that applies to a variety of testing scenarios and requires few assumptions. The main downfall of the permutation test is the excessive computation time required to run such a test making it impractical in some settings and unusable in others. We rectify this via application of variants of the Kahane-Khintchine inequality to construct an analytic upper bound on the permutation test p-value. Our method applies to two-sample and k-sample testing for univariate, multivariate, and functional data. We demonstrate its usefulness on a dataset of spoken phonemes, which makes use of two experimental designs: the Latin square design and the randomized block design.