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Common Statistical Approach
Published in Atsushi Kawaguchi, Multivariate Analysis for Neuroimaging Data, 2021
Thus, a test method that does not depend on the theoretical distribution is useful and the permutation test performs it. The permutation test creates a null distribution using random numbers generated by a computer and performs a statistical hypothesis test based on it. Here, GLM is used for explanation in Figure 3.11. Suppose there is one voxel value for a total of 10 cases, 5 cases and 5 control cases. In the GLM, Y is a voxel value and the design matrix X is a binary value representing a group of Case or Control, however, the intercept is omitted. In this example, the regression coefficient (mean value difference) is 1.006, the standard error is 0.524 and the test statistic T = 1.921 is calculated. Here, the voxel value Y is left as it is and the order of the subjects in X is randomly changed. The resulting design matrix is Shuffle 1. Calculating the test statistic again from this and the GLM for Y yields T = 3.339. By repeating the random replacement 1000 times, 1000 corresponding test statistics can be obtained.
Machine learning for radiation oncology
Published in Jun Deng, Lei Xing, Big Data in Radiation Oncology, 2019
The permutation test is a process repeated a very large number of times in an attempt to establish whether the error estimate obtained on the true data is truly different from those obtained on large numbers of “bogus” data sets, which are created by taking the genuine samples and randomly choosing to either leave their label intact or switch them. Repeated k-fold CV is intended to perform multiple runs of simple resampling schemes to obtain more stable estimates of an algorithm’s performance and enhance the replicability of the results. [33]
Permutation Tests and Nonparametric Combination Methodology
Published in Corain Livio, Arboretti Rosa, Bonnini Stefano, Ranking of Multivariate Populations, 2017
Corain Livio, Arboretti Rosa, Bonnini Stefano
When compared with the more traditional parametric or nonparametric rank-based solutions, the main advantages of using the permutation approach in hypothesis testing problems are that in general permutation tests require fewer and easy to justify assumptions, are exact in nature and offer flexible solutions in dealing with complex problems. In this respect, the permutation-based solution for a complex problem such as the comparison of interventions in Group Randomized Trials (GRTs) is able to maintain a nominal test size thanks to its intrinsic exactness also in case of small sample sizes that usually occur in real applications but are not sufficient to make possible using asymptotic approximations (Braun and Feng, 2001). A simulation study described in the same paper, proves that in the case of the usual realistic sample sizes some traditional asymptotic-based procedures for the problem at hand (Generalized Estimating Equations [GEEs]) have liberal sizes; that is, they do not maintain the nominal level. Moreover, when considering a suitable model-based testing procedure (Penalized Quasi-Likelihood [PQL]) even if it is slightly more powerful than the permutation tests when the model of the simulated data exactly corresponds to that assumed, it is outperformed by the permutation tests when there are too few clusters to support asymptotic methods. In summary, permutation tests for GRTs are appropriate and solutions are more general and powerful than asymptotic counterparts in that they require fewer distributional assumptions. The use of permutation tests is becoming increasingly popular in biomedical research thanks in part to the effective debate within the community of biostatisticians. In a popular paper, Ludbrook and Dudley (1998) argued that, because randomization rather than random sampling is the norm in biomedical research and because group sizes are usually small, exact permutation or randomization tests for differences in location should be preferred over t or F-tests. In this connection, when selecting the more appropriate test statistic and in the planning of the size of a study, Weinberg and Lagakos (2000) derived the asymptotic distribution of permutation tests under a general contiguous alternative, and then investigated the implications for test selection and study design for several diverse areas of biomedical applications.
Effects of Seated Postural Sway on Visually Induced Motion Sickness: A Multiple Regression and RUSBoost Classification Approach
Published in International Journal of Human–Computer Interaction, 2023
In this study, we used RUSBoost for classification. RUSBoost is an effective algorithm that addresses problems of class imbalance. Classifiers were trained by the following features: and gender. The detailed RUSBoost parameters were as follows: number of learner: 50 and learning rate: 0.0328. To design and train the RUSBoost, we used the Classification Learner App from the Matlab toolbox (2020b, Mathworks Inc., Natick, MA, USA). We trained the RUSBoost using this app, optimizing the parameters, and validated our results with 5-fold cross-validation. The following variables were used to present the performance of classification: accuracy, recall, precision, and F-1 score. We also conducted a permutation test for classification accuracy (Ojala & Garriga, 2010). Randomized versions of the training data were obtained by applying independent permutations to each functional element in the original training data, and then 5-fold cross-validation was performed on the permuted training data to generate classification accuracy. After repeating the process 10,000 times, the empirical distribution of the generated accuracy under the null hypothesis was obtained. The p-value for the permutation test was defined as the proportion of the number of permutations in the null distribution that exceeded the accuracy originally obtained from the training data, to the total number of permutations.
Understanding knowledge workers’ job performance: a perspective of online and offline communication networks
Published in Enterprise Information Systems, 2019
Fei Gao, Junwei Wang, Shiquan Wang
Therefore, consistent with prior research (e.g., Badar, Hite, and Badir 2013; Císař and Navrátil 2015; Neumeyer, He, and Santos 2017), we applied the node-level regression procedure provided in UCINET 6.620 (Borgatti, Everett, and Freeman 2002) to analyze the network data. The regression algorithm proceeded in two steps. In the first step, a standard multiple regression was performed. In the second step, permutation test, which does not involve samples, was carried out to construct the p-value. The general logic of permutation test is to calculate all the ways that the test could have come out given that variables were actually independent, and compute the p-value as a proportion of random assignments yielding a statistic as large as the one actually observed. This kind of test provides an elegant and powerful way to address the special issues posed by network data, such as collinearity and working with all network actors (Borgatti, Everett, and Johnson 2013). The final estimates could be interpreted in the same way as those obtained from standard regressions (Krackhardt 1988).
Gaze Interaction With Vibrotactile Feedback: Review and Design Guidelines
Published in Human–Computer Interaction, 2020
Jussi Rantala, Päivi Majaranta, Jari Kangas, Poika Isokoski, Deepak Akkil, Oleg Špakov, Roope Raisamo
The argument is that if the null hypothesis is true, then all possible permutations of the data are equally likely, and the observed sample is just one of them and should appear as a typical value. If this does not seem to be the case (the observed test statistics value is rather extreme, there are only a few equally extreme or more extreme values), then the null hypothesis probably is not true. The permutation test principle is very general and does not depend on assumptions on the normality of samples, random sampling, or independence of observations.