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Analysis of similarities (ANOSIM) for 2‐way layouts using a generalised ANOSIM statistic, with comparative notes on Permutational Multivariate Analysis of Variance (PERMANOVA)

Paul J. Somerfield, K. Robert Clarke, Ray N. Gorley
2021 Austral ecology (Print)  
The generalised ANOSIM statistic R O is defined as the slope of the linear regression of ranked resemblances from observations against ranked distances in a model describing the unordered or ordered distances  ...  In the absence of ordering, this becomes the standard ANOSIM R statistic.  ...  It should be noted that PERMANOVA and ANO-SIM also differthough less markedlyeven for the one-way case, in terms of their null hypotheses, interpretation and response of the statistics to differences in  ... 
doi:10.1111/aec.13059 fatcat:ypiq5pn43fdnngob2c7un6r7ve

A Counter Example to the Shuffle Compatiblity Conjecture [article]

Ezgi Kantarcı Oğuz
2018 arXiv   pre-print
They further conjectured that any shuffle compatible permutation statistic is a descent statistic. In this note we construct a counter-example to this conjecture.  ...  The shuffle product has a connection with several useful permutation statistics such as descent and peak, and corresponds to the multiplication operation in the corresponding descent and peak algebras.  ...  A function st on permutations is said to be a permutation statistic if st(σ) = st(φ) whenever σ ∼ φ.  ... 
arXiv:1807.01398v1 fatcat:ywiggdrbufe2nig2vzqivpjxxe

Robust nonparametric tests of general linear model coefficients: A comparison of permutation methods and test statistics

Nathaniel E. Helwig
2019 NeuroImage  
Statistical inference in neuroimaging research often involves testing the significance of regression coefficients in a general linear model.  ...  This study compares the classic F test statistic to the robust W (Wald) test statistic using eight different permutation methods.  ...  Acknowledgements Funded by a Single Semester Leave award from the University of Minnesota and NIH grants 1U01MH108150-01A1 and 1R01MH112583-01A1.  ... 
doi:10.1016/j.neuroimage.2019.116030 pmid:31330243 pmcid:PMC6765412 fatcat:27rmvdrckbfvjcvqdqvozyaapu

On joint distribution of adjacencies, descents and some Mahonian statistics

Alexander Burstein
2010 Discrete Mathematics & Theoretical Computer Science  
We also prove Eriksen's conjecture that a certain bistatistic on Viennot's alternative tableaux is Euler-Mahonian.  ...  descents and some Mahonian statistics.  ...  Introduction Eriksen [3] defined a new statistic adj on permutations that has the same distribution as the number of fixed points.  ... 
doi:10.46298/dmtcs.2846 fatcat:3am72fjprnehrg4gwmvy2oubty

Stable multivariate Eulerian polynomials and generalized Stirling permutations

J. Haglund, Mirkó Visontai
2012 European journal of combinatorics (Print)  
We study Eulerian polynomials as the generating polynomials of the descent statistic over Stirling permutations-a class of restricted multiset permutations.  ...  Second, we obtain simpler recurrences of a general pattern, which allows for essentially a single proof of stability for all the cases, and further proofs of equidistributions among different statistics  ...  Previous work Statistics on permutations and Stirling permutations Let n be a positive integer, and let S n denote the set of all permutations of the set {1, . . . , n}.  ... 
doi:10.1016/j.ejc.2011.10.007 fatcat:oz44bwgtqna3ta4venhm2p75he

Interaction Testing: Residuals-Based Permutations and Parametric Bootstrap in Continuous, Count, and Binary Data

Petra Buzkova
2016 Epidemiologic Methods  
AbstractTo obtain statistical inference about interaction hypotheses without making strong distributional assumptions, permutation tests based on permuting the outcomes are often being used.  ...  It was shown that in continuous and binary data these tests might not be even approximately valid and parametric bootstrap was suggested as a viable alternative, outperforming such permutation tests.  ...  We note that the test statistic s o from the original data is considered a permutation statistic in p-value calculation in (7). It is not used as such in the parametric bootstrap in (8).  ... 
doi:10.1515/em-2015-0010 fatcat:g5hvpl2irfaj5ojiviebymtsbq

GSA-Lightning: ultra-fast permutation-based gene set analysis

Billy Heung Wing Chang, Weidong Tian
2016 Bioinformatics  
This article introduces GSA-Lightning, a fast implementation of permutation-based gene set analysis.  ...  Availability and implementation: The GSA-Lightning R package is available on Github at https:// github.com/billyhw/GSALightning and on R Bioconductor.  ...  Acknowledgements We thank Xinran Dong for providing earlier speed benchmarking results, and the anonymous reviewers for helpful comments on the article and the R package.  ... 
doi:10.1093/bioinformatics/btw349 pmid:27296982 fatcat:dplqkzcwj5gxpbbep53qzg43je

Permutations that preserve asymptotically null sets and statistical convergence

Jeff Connor
2020 Filomat  
We then show that a permutation has this property if and only if it maps statistically convergent sequences into statistically convergent sequences.  ...  The main result of this article is a characterization of the permutations ?: N ?  ...  We also note that the preceding work can be used to establish the analogous result that, given a permutation θ, one can show that the statistical convergence of θx implies the statistical convergence of  ... 
doi:10.2298/fil2014821c fatcat:45abab4shbgqfe6osck6ku6q7m

An interesting new Mahonian permutation statistic [article]

Mark C. Wilson
2010 arXiv   pre-print
The standard algorithm for generating a random permutation gives rise to an obvious permutation statistic that is readily seen to be Mahonian.  ...  Several ideas for further research on this topic are listed.  ...  For our purposes a permutation statistic is simply a function T : S → N. Of course it is always possible to construct a statistic T by for each n making it equal to a given statistic T n on S n .  ... 
arXiv:1007.3560v1 fatcat:tven24zla5bkdiynwfjzmke46u

A Permutation Test for Unit Root in an Autoregressive Model

Jiexiang Li, Lanh Tran, Sa-aat Niwitpong
2013 Applied Mathematics  
A permutation test (based on a finite random sample of permutations) for unit root in an autoregressive process is considered.  ...  Simulations show that the power of the permutation test is reasonable when sample sizes are small or when the white noises have a heavy tailed distribution. The test is shown to be consistent.  ...  For some literature on tests for serial dependence, see [3] and [4] H holds, we propose a permutation test for unit root using n as our pivot test statistic.  ... 
doi:10.4236/am.2013.412221 fatcat:tbtr5vge75gr3hffwtyff7kyp4

Nonparametric permutation tests for functional neuroimaging: A primer with examples

Thomas E. Nichols, Andrew P. Holmes
2001 Human Brain Mapping  
When the appropriate assumptions hold, the nonparametric permutation approach gives results similar to those obtained from a comparable Statistical Parametric Mapping approach using a general linear model  ...  Requiring only minimal assumptions for validity, nonparametric permutation testing provides a flexible and intuitive methodology for the statistical analysis of data from functional neuroimaging experiments  ...  ACKNOWLEDGMENTS We thank the authors of the three example data sets analyzed for permission to use their data; to Karl Friston and Ian Ford for statistical advice; to the two anonymous reviewers for their  ... 
doi:10.1002/hbm.1058 pmid:11747097 fatcat:fytq6xmepje45cznb3h4yakize

Comparison of Randomization method for RV coefficient and Permutation Method for Hotelling T-Squared

Charles Aronu, Godday Ebuh, Cecilia Okoli, Rose Nwosu
2014 SOP Transactions on Statistics and Analysis  
of 0.00 which fall on the rejection region of the hypothesis assuming a 95% confidence level.  ...  measure T 2 was 6.04 and a corresponding P-value of 0.00 which falls on the rejection region of the hypothesis assuming a 95% confidence level.  ...  However, [11] , noted that in the permutation model, an expected distribution of a given association statistic is generated by repeatedly randomizing one of the initial distance matrices and calculating  ... 
doi:10.15764/stsa.2014.02003 fatcat:gg3zp5zl7ram3dekn3j3e5xcre

An evaluation of traditional and novel tools for lesion behavior mapping

C RORDEN, J FRIDRIKSSON, H KARNATH
2009 NeuroImage  
Furthermore, on theoretical grounds we suggest that permutation-based thresholding will be a more sensitive method for controlling familywise error than the method of counting lesion-overlap clusters used  ...  The authors correctly note that their procedure can offer substantially more statistical power than conventional LBM methods.  ...  Our software (NPM; Rorden et al. 2007 ) implemented a novel form of permutation thresholding: conducting one statistical test for each DLP, rather than for each lesion.  ... 
doi:10.1016/j.neuroimage.2008.09.031 pmid:18950719 pmcid:PMC2667945 fatcat:a45i7xxmlrg2fch2xtwl6ull3e

Permutation Testing for Treatment–Covariate Interactions and Subgroup Identification

Jared C. Foster, Bin Nan, Lei Shen, Niko Kaciroti, Jeremy M. G. Taylor
2015 Statistics in Biosciences  
The proposed methods are shown to outperform traditional permutation methods in a simulation study.  ...  In such cases, it is natural to consider permutation-based tests, which shuffle selected parts of the data in order to remove one or more associations of interest; however, in the case of interactions,  ...  Acknowledgments This research was partially supported by a grant from Eli Lilly, grant DMS-1007590 from the National Science Foundation, grants CA083654 and AG036802 from the National Institutes of Health  ... 
doi:10.1007/s12561-015-9125-9 pmid:27606036 pmcid:PMC5010868 fatcat:f4uxl7mpqbbnbm5bzclqfb74ki

An Interesting New Mahonian Permutation Statistic

Mark C. Wilson
2010 Electronic Journal of Combinatorics  
The standard algorithm for generating a random permutation gives rise to an obvious permutation statistic DIS that is readily seen to be Mahonian.  ...  Several ideas for further research on this topic are listed.  ...  For our purposes a permutation statistic is simply a function T : S → N. Of course it is always possible to construct a statistic T by for each n making it equal to a given statistic T n on S n .  ... 
doi:10.37236/419 fatcat:c6pm435funfotopfoflv5eiy3i
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