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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)

2021
*
Austral ecology (Print)
*

The generalised ANOSIM

doi:10.1111/aec.13059
fatcat:ypiq5pn43fdnngob2c7un6r7ve
*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 ...##
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A Counter Example to the Shuffle Compatiblity Conjecture
[article]

2018
*
arXiv
*
pre-print

They further conjectured that any shuffle compatible

arXiv:1807.01398v1
fatcat:ywiggdrbufe2nig2vzqivpjxxe
*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. ...##
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Robust nonparametric tests of general linear model coefficients: A comparison of permutation methods and test statistics

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. ...

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On joint distribution of adjacencies, descents and some Mahonian statistics

2010
*
Discrete Mathematics & Theoretical Computer Science
*

We also prove Eriksen's conjecture that

doi:10.46298/dmtcs.2846
fatcat:3am72fjprnehrg4gwmvy2oubty
*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. ...##
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Stable multivariate Eulerian polynomials and generalized Stirling permutations

2012
*
European journal of combinatorics (Print)
*

We study Eulerian polynomials as the generating polynomials of the descent

doi:10.1016/j.ejc.2011.10.007
fatcat:oz44bwgtqna3ta4venhm2p75he
*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}. ...##
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Interaction Testing: Residuals-Based Permutations and Parametric Bootstrap in Continuous, Count, and Binary Data

2016
*
Epidemiologic Methods
*

AbstractTo obtain

doi:10.1515/em-2015-0010
fatcat:g5hvpl2irfaj5ojiviebymtsbq
*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). ...##
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GSA-Lightning: ultra-fast permutation-based gene set analysis

2016
*
Bioinformatics
*

This article introduces GSA-Lightning,

doi:10.1093/bioinformatics/btw349
pmid:27296982
fatcat:dplqkzcwj5gxpbbep53qzg43je
*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. ...##
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Permutations that preserve asymptotically null sets and statistical convergence

2020
*
Filomat
*

We then show that

doi:10.2298/fil2014821c
fatcat:45abab4shbgqfe6osck6ku6q7m
*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 ...##
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An interesting new Mahonian permutation statistic
[article]

2010
*
arXiv
*
pre-print

The standard algorithm for generating

arXiv:1007.3560v1
fatcat:tven24zla5bkdiynwfjzmke46u
*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 . ...##
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A Permutation Test for Unit Root in an Autoregressive Model

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*. ...

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Nonparametric permutation tests for functional neuroimaging: A primer with examples

2001
*
Human Brain Mapping
*

When the appropriate assumptions hold, the nonparametric

doi:10.1002/hbm.1058
pmid:11747097
fatcat:fytq6xmepje45cznb3h4yakize
*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 ...##
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Comparison of Randomization method for RV coefficient and Permutation Method for Hotelling T-Squared

2014
*
SOP Transactions on Statistics and Analysis
*

of 0.00 which fall

doi:10.15764/stsa.2014.02003
fatcat:gg3zp5zl7ram3dekn3j3e5xcre
*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 ...##
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An evaluation of traditional and novel tools for lesion behavior mapping

2009
*
NeuroImage
*

Furthermore,

doi:10.1016/j.neuroimage.2008.09.031
pmid:18950719
pmcid:PMC2667945
fatcat:a45i7xxmlrg2fch2xtwl6ull3e
*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. ...##
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Permutation Testing for Treatment–Covariate Interactions and Subgroup Identification

2015
*
Statistics in Biosciences
*

The proposed methods are shown to outperform traditional

doi:10.1007/s12561-015-9125-9
pmid:27606036
pmcid:PMC5010868
fatcat:f4uxl7mpqbbnbm5bzclqfb74ki
*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 ...##
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An Interesting New Mahonian Permutation Statistic

2010
*
Electronic Journal of Combinatorics
*

The standard algorithm for generating

doi:10.37236/419
fatcat:c6pm435funfotopfoflv5eiy3i
*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 . ...
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