Permutation tests for univariate or multivariate analysis of variance and regression

2001 ◽  
Vol 58 (3) ◽  
pp. 626-639 ◽  
Author(s):  
Marti J Anderson
Keyword(s):  
Analysis Of Variance ◽  
Linear Models ◽  
Permutation Test ◽  
Permutation Tests ◽  
Random Allocation ◽  
Partial Regression ◽  
Permutation Distribution ◽  
Exact Test ◽  
Restricted Permutation ◽  
Theoretical Results

The most appropriate strategy to be used to create a permutation distribution for tests of individual terms in complex experimental designs is currently unclear. There are often many possibilities, including restricted permutation or permutation of some form of residuals. This paper provides a summary of recent empirical and theoretical results concerning available methods and gives recommendations for their use in univariate and multivariate applications. The focus of the paper is on complex designs in analysis of variance and multiple regression (i.e., linear models). The assumption of exchangeability required for a permutation test is assured by random allocation of treatments to units in experimental work. For observational data, exchangeability is tantamount to the assumption of independent and identically distributed errors under a null hypothesis. For partial regression, the method of permutation of residuals under a reduced model has been shown to provide the best test. For analysis of variance, one must first identify exchangeable units by considering expected mean squares. Then, one may generally produce either (i) an exact test by restricting permutations or (ii) an approximate test by permuting raw data or some form of residuals. The latter can provide a more powerful test in many situations.

scholarly journals Permutation tests for comparative data

2020 ◽  
Author(s):  
James G. Saulsbury
Keyword(s):  
Least Squares ◽  
Permutation Test ◽  
Phylogenetic Signal ◽  
Cyclic Permutation ◽  
Permutation Tests ◽  
Generalized Least Squares ◽  
Comparative Data ◽  
Least Squares Regression ◽  
Data Points ◽  
Restricted Permutation

AbstractThe analysis of patterns in comparative data has come to be dominated by least-squares regression, mainly as implemented in phylogenetic generalized least-squares (PGLS). This approach has two main drawbacks: it makes relatively restrictive assumptions about distributions and can only address questions about the conditional mean of one variable as a function of other variables. Here I introduce two new non-parametric constructs for the analysis of a broader range of comparative questions: phylogenetic permutation tests, based on cyclic permutations and permutations conserving phylogenetic signal. The cyclic permutation test, an extension of the restricted permutation test that performs exchanges by rotating nodes on the phylogeny, performs well within and outside the bounds where PGLS is applicable but can only be used for balanced trees. The signal-based permutation test has identical statistical properties and works with all trees. The statistical performance of these tests compares favorably with independent contrasts and surpasses that of a previously developed permutation test that exchanges closely related pairs of observations more frequently. Three case studies illustrate the use of phylogenetic permutations for quantile regression with non-normal and heteroscedastic data, testing hypotheses about morphospace occupation, and comparative problems in which the data points are not tips in the phylogeny.

scholarly journals Optimized permutation testing for information theoretic measures of multi-gene interactions

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
James M. Kunert-Graf ◽  
Nikita A. Sakhanenko ◽  
David J. Galas
Keyword(s):  
Large Scale ◽  
Permutation Test ◽  
Association Studies ◽  
Genome Wide Association Studies ◽  
Permutation Testing ◽  
Exact Test ◽  
Information Theoretic ◽  
Information Theoretic Measures ◽  
Full Analysis ◽  
Computational Bottleneck

Abstract Background Permutation testing is often considered the “gold standard” for multi-test significance analysis, as it is an exact test requiring few assumptions about the distribution being computed. However, it can be computationally very expensive, particularly in its naive form in which the full analysis pipeline is re-run after permuting the phenotype labels. This can become intractable in multi-locus genome-wide association studies (GWAS), in which the number of potential interactions to be tested is combinatorially large. Results In this paper, we develop an approach for permutation testing in multi-locus GWAS, specifically focusing on SNP–SNP-phenotype interactions using multivariable measures that can be computed from frequency count tables, such as those based in Information Theory. We find that the computational bottleneck in this process is the construction of the count tables themselves, and that this step can be eliminated at each iteration of the permutation testing by transforming the count tables directly. This leads to a speed-up by a factor of over 103 for a typical permutation test compared to the naive approach. Additionally, this approach is insensitive to the number of samples making it suitable for datasets with large number of samples. Conclusions The proliferation of large-scale datasets with genotype data for hundreds of thousands of individuals enables new and more powerful approaches for the detection of multi-locus genotype-phenotype interactions. Our approach significantly improves the computational tractability of permutation testing for these studies. Moreover, our approach is insensitive to the large number of samples in these modern datasets. The code for performing these computations and replicating the figures in this paper is freely available at https://github.com/kunert/permute-counts.

scholarly journals Parallelized calculation of permutation tests

2020 ◽  
Author(s):  
Markus Ekvall ◽  
Michael Höhle ◽  
Lukas Käll
Keyword(s):  
Dynamic Programming ◽  
Sample Size ◽  
Permutation Test ◽  
Statistical Tests ◽  
Permutation Tests ◽  
Supplementary Information ◽  
Attractive Alternative ◽  
Test Statistic ◽  
Sample Distribution ◽  
Running Time

Abstract Motivation Permutation tests offer a straightforward framework to assess the significance of differences in sample statistics. A significant advantage of permutation tests are the relatively few assumptions about the distribution of the test statistic are needed, as they rely on the assumption of exchangeability of the group labels. They have great value, as they allow a sensitivity analysis to determine the extent to which the assumed broad sample distribution of the test statistic applies. However, in this situation, permutation tests are rarely applied because the running time of naïve implementations is too slow and grows exponentially with the sample size. Nevertheless, continued development in the 1980s introduced dynamic programming algorithms that compute exact permutation tests in polynomial time. Albeit this significant running time reduction, the exact test has not yet become one of the predominant statistical tests for medium sample size. Here, we propose a computational parallelization of one such dynamic programming-based permutation test, the Green algorithm, which makes the permutation test more attractive. Results Parallelization of the Green algorithm was found possible by non-trivial rearrangement of the structure of the algorithm. A speed-up—by orders of magnitude—is achievable by executing the parallelized algorithm on a GPU. We demonstrate that the execution time essentially becomes a non-issue for sample sizes, even as high as hundreds of samples. This improvement makes our method an attractive alternative to, e.g. the widely used asymptotic Mann-Whitney U-test. Availabilityand implementation In Python 3 code from the GitHub repository https://github.com/statisticalbiotechnology/parallelPermutationTest under an Apache 2.0 license. Supplementary information Supplementary data are available at Bioinformatics online.

Επίδραση αναλόγου της προστακυκλίνης στην επούλωση αναστομώσεων του παχέος εντέρου επίμυων σε συνθήκες αποφρακτικού ειλεού

2012 ◽  
Author(s):  
Γεώργιος Γαλανόπουλος
Keyword(s):  
Analysis Of Variance ◽  
Anova Analysis ◽  
Exact Test ◽  
Fisher's Exact Test ◽  
Significant Difference ◽  
Fisher’S Exact Test

Στόχος της παρούσας διδακτορικής διατριβής ήταν η πειραματική μελέτη της επίδρασης της ιλοπρόστης (ανάλογο της προστακυκλίνης) στην επούλωση αναστομώσεων του παχέος εντέρου επίμυων σε συνθήκες αποφρακτικού ειλεού. Για τη μελέτη χρησιμοποιήθηκαν 80 άρρενες επίμυες, οι οποίοι χωρίστηκαν τυχαιοποιημένα σε 4 (1, 2, 3, 4) ομάδες, με 2 (α, β) ισοδύναμες υποομάδες έκαστη. Στην ομάδα 1 (ελέγχου) και 3 (ιλοπρόστη) διενεργήθηκε τμηματική εντερεκτομή και τελικοτελική αναστόμωση. Στην ομάδα 2 (ειλεός) και 4 (ειλεός και ιλοπρόστη) επιτεύχθηκαν αρχικά συνθήκες αποφρακτικού ειλεού και 24 ώρες μετά διενεργήθηκε τμηματική εντερεκτομή και τελικοτελική αναστόμωση. Η ιλοπρόστη χορηγήθηκε στις ομάδες 3 και 4 σε δόση 2μg/kg Β.Σ. σε 3ml διαλύματος NaCl 0,9% ενδοπεριτοναϊκά, διεγχειρητικά και κάθε ημέρα μέχρι τη θυσία, ενώ αντίστοιχα στις ομάδες 1 και 2 στα πειραματόζωα χορηγούνταν 3ml διαλύματος NaCl 0,9%. Σε κάθε ομάδα τα μισά πειραματόζωα (υποομάδα 1α, 2α, 3α, 4α) θυσιάστηκαν την 4η μετεγχειρητική ημέρα και τα υπόλοιπα (υποομάδα 1β, 2β, 3β, 4β) την 8η. Κατά τη νεκροτομή γινόταν μακροσκοπικός έλεγχος για ρήξη της αναστόμωσης, ύπαρξη περιτονίτιδος ή περιαναστομωτικού αποστήματος καθώς και ποσοτική αξιολόγηση των συμφύσεων σύμφωνα με την κλίμακα Van der Hamm. Ακολουθούσε μέτρηση της πίεσης διάσπασης και στη συνέχεια τμήμα της αναστόμωσης αποστέλλονταν για ιστολογική εξέταση κατά την οποία αξιολογούνταν η φλεγμονώδης αντίδραση (διήθηση από ουδετερόφιλα), η νεοαγγειογένεση, ο αριθμός των ινοβλαστών και η εναπόθεση νεοκολλαγόνου. Η ταξινόμηση των μικροσκοπικών ευρημάτων έγινε σύμφωνα με την κλίμακα Ehrlich και Hunt με τις τροποποιήσεις κατά Phillips. Επιπλέον, προσδιορίστηκε βιοχημικά η συγκέντρωση υδροξυπρολίνης και κολλαγενάσης I επί της αναστόμωσης. Για την συνοπτική παρουσίαση των αποτελεσμάτων υπολογίστηκαν απόλυτες και σχετικές συχνότητες (ποσοστά %), δείκτες κεντρικής τάσης (μέσοι όροι, διάμεσες τιμές) και δείκτες διασποράς (ελάχιστες τιμές, μέγιστες τιμές, τυπικές αποκλίσεις). Για τη σύγκριση των μέσων όρων χρησιμοποιήθηκε το κριτήριο της Ελάχιστης Σημαντικής Διαφοράς (Least Significant Difference-LSD), μετά από την εφαρμογή της μεθόδου ANOVA (Analysis of Variance). Για τις συγκρίσεις των ποσοστών, εφαρμόστηκε ο ακριβής έλεγχος του Fisher (Fisher’s Exact Test). Από την ανάλυση των πειραματικών δεδομένων προέκυψε ότι η ενδοπεριτοναϊκή χορήγηση ιλοπρόστης σε συνθήκες αποφρακτικού ειλεού, έχει ως αποτέλεσμα τον περιορισμό της αρνητικής δράσης του ειλεού στην επούλωση των αναστομώσεων του παχέος εντέρου. Συγκεκριμένα, την 4η και 8η μετεγχειρητική ημέρα ελαττώνει σημαντικά την απώλεια σωματικού βάρους. Επίσης, προάγει τη νεοαγγειογένεση, ενώ συγχρόνως αυξάνει τον πολλαπλασιασμό των ινοβλαστών και τη συγκέντρωση υδροξυπρολίνης. Επιπλέον, την 4η μετεγχειρητική ημέρα ελαττώνει τη φλεγμονώδη αντίδραση και μειώνει τη συγκέντρωση κολλαγενάσης Ι. Σταδιακά, την 8η μετεγχειρητική ημέρα αυξάνει τη σύνθεση νεοκολλαγόνου στην περιοχή της αναστόμωσης. Οι παραπάνω δράσεις έχουν ως αποτέλεσμα την αύξηση της μηχανικής ισχύος των αναστομώσεων, κατά την 4η και 8η μετεγχειρητική ημέρα, όπως αυτή προκύπτει από τη μέτρηση των πιέσεων διάσπασης. Συμπερασματικά, η άμεση μετεγχειρητική ενδοπεριτοναϊκή χορήγηση ιλοπρόστης ενισχύει τους μηχανισμούς επούλωσης και αντισταθμίζει την αρνητική δράση του ειλεού στην επούλωση των αναστομώσεων του παχέος εντέρου.

scholarly journals Drawing inferences for high‐dimensional linear models: A selection‐assisted partial regression and smoothing approach

Biometrics ◽  
2019 ◽  
Vol 75 (2) ◽  
pp. 551-561
Author(s):  
Zhe Fei ◽  
Ji Zhu ◽  
Moulinath Banerjee ◽  
Yi Li
Keyword(s):  
Linear Models ◽  
High Dimensional ◽  
Partial Regression

scholarly journals Estimating Bayes factors from minimal summary statistics in repeated measures analysis of variance designs

2020 ◽  
Vol 17 (1) ◽  
Author(s):  
Thomas Faulkenberry
Keyword(s):  
Analysis Of Variance ◽  
Repeated Measures ◽  
Bayes Factor ◽  
Linear Models ◽  
Repeated Measurements ◽  
Bayes Factors ◽  
Complex Method ◽  
Summary Statistics ◽  
Minimal Set ◽  
Repeated Measures Analysis

In this paper, I develop a formula for estimating Bayes factors directly from minimal summary statistics produced in repeated measures analysis of variance designs. The formula, which requires knowing only the F-statistic, the number of subjects, and the number of repeated measurements per subject, is based on the BIC approximation of the Bayes factor, a common default method for Bayesian computation with linear models. In addition to providing computational examples, I report a simulation study in which I demonstrate that the formula compares favorably to a recently developed, more complex method that accounts for correlation between repeated measurements. The minimal BIC method provides a simple way for researchers to estimate Bayes factors from a minimal set of summary statistics, giving users a powerful index for estimating the evidential value of not only their own data, but also the data reported in published studies.

scholarly journals Air Rebusan Seledri Menurunkan Tekanan Darah

2015 ◽  
Vol 6 (2) ◽  
Author(s):  
Wiwik Afridah ◽  
Budi Setiawan
Keyword(s):  
Blood Pressure ◽  
Elderly People ◽  
Elderly Population ◽  
Fruits And Vegetables ◽  
Healthy Lifestyle ◽  
Control Group ◽  
Fisher Exact Test ◽  
Random Allocation ◽  
Test Results ◽  
Exact Test

The increasing elderly population will lead to problems such as health problems, one of which is hypertension. The purpose of this study was to determine the effect of celery stew on blood pressure in elderly people with hypertension Hulaan Village District Menganti Gresik regency. This study uses a design Case control design with the aging population in the first level of hypertension by 12 people, with a large sample of elderly with hypertension entire first level is 12 people, and how to use the total sampling sampling and divided into 6 groups of 6 cases and the control group with random allocation techniques. Celery stew independent variables and the dependent variable blood pressure. The data was collected by means of measuring the blood pressure recorded recapitulation and analyzed using the Fisher exact test with α = 0.05. The research results obtained from 6 groups of cases that were given celery stew all experienced a decrease in blood pressure, whereas in the control group of 6 people who were not given celery stew is only 1 person that declined. Fisher Exact test results obtained ρ (0.015) <α (0.05), means that the research hypothesis is accepted ie no celery stew effect on blood pressure in elderly people with hypertension Hulaan Village District Menganti Gresik Regency. The conclusions of this study are no celery stew effect on blood pressure of elderly with hypertension. Hypertensive patients are expected to maintain your diet, multiply to consume fruits and vegetables that contain potassium, as well as a healthy lifestyle change. 

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