Testes de permutação ou aleatorização no r-permanova

Abstract

Permutation and randomization tests are widely used in ecology studies, where the variables usually consist of abundance counts (or percentage coverage, frequencies or biomass) for a large number of species, but can also be used in other areas. Computationally intensive methods for statistical inference are used when traditional approaches are not adequate. These being the permutation or randomization tests, where the basic idea implicit in these tests is to calculate a test statistic for each permutation of the data, in order to build the reference set from which the probability associated with the statistic is determined. observed test. For such permutation and randomization procedures, it is not necessary to establish assumptions about the theoretical distribution, being considered distribution-free tests. However, they have limitations, they can only be used for hypotheses that involve comparisons (swapping observations between groups) or misaligned records (as in correlation, for example) or hypotheses that say that the observations for a group are in a random order (where randomization involves the generation of alternative random orders). Therefore, they cannot be used to test hypotheses about individual parameters. These tests are based on ANOVA for multivariate analysis based on permutation. In the R software we have the tests "PERMANOVA"and "ANOSIM"for testing the permutation of a distance matrix involving a categorical variable. In addition to the "Mantel test", which consists of calculating the correlation between two matrices, based on the permutation. These tests can be found in the “vegan: Community Ecology Package”. For linear models, permutation tests are useful when the assumption of normality is violated or when the sample size is too small to apply asymptotic theory. These are typical significance tests where the tested statistical distribution is obtained by calculating all possible values of this statistic rearranging the sample values considering a true null hypothesis, being a way to determine if the value of the null hypothesis is reasonable. Thus, the main objective of this work is to present some tests based on permutation or randomization, applied in two cases. In situation for a matrix-group and the second for two groups, with two matrices.