Permutation tests

Zhao ]H, Curtis D, Sham PC. Model-free analysis and permutation tests for allelic associations. Hum Hered 2000 50[2] 133—139. 

We will refer to pathways that have become significantly cohesive in tumor tissues as up pathways, and those that have lost their coherence in tumor tissues as down pathways. Random permutation tests to examine the probability of observing up and down pathways by chance show that our observation of down pathways is significantly higher than random p = 0.002). These results indicate that pathways tend to become less cohesive in tumor tissues than in normal tissues. 

Ordination axes are determined sequentially. The first axis is calculated to account for the most prominent variance in the samples or species subsequent axes are calculated to account for variability not explained by the earlier axes. It is useful to visualize the distribution of samples or species as a function of their scores on the two or three most significant axes (as represented by their eigenvalues and testable by permutation tests). Plots of one ordination axis versus another (called bivariate plots or biplots) can be used to examine patterns of similarity and difference among species and samples. 

The t-test analysis computes for each gene the probability that the difference between the mean fluorescence intensities of the test and reference samples is falsely called significant (p-value), by theoretical t-distribution or permutation test. 

Disadvantages are that these response surface models are not available in standard software packages. Like all nonlinear statistical methods, the methodology is still subject to research, which has 2 important consequences. First, correlation structure of the parameters in these nonlinear models is usually not addressed. Second, the assessment of the test statistic is based on approximate statistical procedures. The statistical analyses can probably be improved through bootstrap analysis or permutation tests. 

Jonathan, P., McCarthy, W.V. and Roberts, A.M. (1996). Discriminant Analysis with Singular Covariance Matrices. A Method Incorporating Cross-Validation and Efficient Randomized Permutation Tests. J.Chemom., 10,189-213. 

Lindgren, R, Hansen, B., Karcher, W., Sjbstrdm, M. and Eriksson, L. (1996). Model Validation by Permutation Tests Applications to Variable Selection. J.Chemom., 10,521-532. 

A technique derived from a principal components approach is the coupling of PCA with redundancy analysis (RDA) (van der Brink et al. 1996). The utility of the technique is that it provides a depiction of the treatment trajectories in an ecological space, and the statistical significance can be examined using a permutation test. One of the proposed benefits of the technique is that it can determine recovery, a dubious distinction in light of the ground work laid in Chapter 2. In common with other PCA techniques, the technique does assume a linear response. 

Good, I.J. 1982. An index of separateness of clusters and a permutation test for its significance. /. Stef. Comput. Simul. 15 81-84. 

Good, P. Permutation tests A practical guide to resampling methods for testing hypotheses. Springer-Verlag, New York, 2000. 

Several procedures are available that evaluate the phylogenetic signal in the data and the robustness of trees (Swofford et al., 1996 Li, 1997). The most popular of the former class are tests of data signal versus randomized data (skewness and permutation tests). The latter class includes tests of tree support from resampling of observed data (nonparametric bootstrap). The likelihood ratio test provides a means of evaluating both the substitution model and the tree. 

Dayhoff, M. O. (1979). Atlas of Protein Sequence and Structure, Volume 5, Supplement 3, 1978. National Biomedical Research Foundation, Washington, D.C.Faith, D. R, and Trueman, 1. W. H. (1996). When the topology-dependent permutation test (T-PTP) for mono-phyly returns significant support for monophyly, should that be equated with (a) rejecting the null hypothesis of nonmonophyly, (b) rejecting the null hypothesis of no structure, (c) failing to falsify a hypothesis of monophyly, or (d) none of the above Syst. Biol. 45, 580-586. 

A.I. Bandos, H.E. Rockette, D. Gur, A permutation test sensitive to differences in areas... 

Dijksterhuis, G. B. and Reiser, W. J. (1995). The role of permutation tests in exploratory multivariate data analysis. Food Quality and Preference, 6, 263-270. 

Xiong, R., Blot, K., Meullenet, J. F. and Dessirier, J. M. (2008). Permutation tests for generalized procrustes analysis. Food Quality and Preference, 19, 146-155. 

The calculation of each index is derived from the usual sum of square decomposition used in ANOVA, but applied to dominance rates. For instance, the discrimination index at panel level is simply the sum of square of the product effect (see the original paper for more details on the other indexes). However, the authors do not follow the F-test approach to test the significance for these indexes, since TDS data (or the residuals from any standard ANOVA model) are not normally distributed. They rather follow the permutation test approach proposed by Meyners and Pineau (2010) and Meyners (2011) and extend it to the scope of their indexes. The reader can refer to the original paper for more details about the testing procedure. 

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