scholarly journals Enlarging the Scope of Randomization and Permutation Tests in Neuroimaging and Neuroscience

2019 ◽  
Author(s):  
Eric Maris
Keyword(s):  
Rate Control ◽  
Explanatory Variable ◽  
Statistical Tests ◽  
Permutation Tests ◽  
Informed Choice ◽  
Companion Paper ◽  
Nonparametric Tests ◽  
Test Statistic ◽  
Drastic Increase ◽  
Nonparametric Statistical

AbstractEspecially for the high-dimensional data collected in neuroscience, nonparametric statistical tests are an excellent alternative for parametric statistical tests. Because of the freedom to use any function of the data as a test statistic, nonparametric tests have the potential for a drastic increase in sensitivity by making a biologically-informed choice for a test statistic. In a companion paper (Geerligs & Maris, 2020), we demonstrate that such a drastic increase is actually possible. This increase in sensitivity is only useful if, at the same time, the false alarm (FA) rate can be controlled. However, for some study types (e.g., within-participant studies), nonparametric tests do not control the FA rate (see Eklund, Nichols, & Knutsson, 2016). In the present paper, we present a family of nonparametric randomization and permutation tests of which we prove exact FA rate control. Crucially, these proofs hold for a much larger family of study types than before, and they include both within-participant studies and studies in which the explanatory variable is not under experimental control. The crucial element of this statistical innovation is the adoption of a novel but highly relevant null hypothesis: statistical independence between the biological and the explanatory variable.

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.

Nonparametric Statistics on the Computer

1969 ◽  
Vol 6 (1) ◽  
pp. 86-92
Author(s):  
John Morris
Keyword(s):  
Missing Data ◽  
Statistical Tests ◽  
Computer Programs ◽  
Nonparametric Statistics ◽  
Nonparametric Tests ◽  
Statistical System ◽  
Nonparametric Statistical

The nonparametric statistical system is a package of computer programs for use with data that may not meet the assumptions of more traditional statistical tests. Thirty-four nonparametric tests are available in the system. Provisions for missing data, variable formats, and other options make the system potentially useful in research based on attitude questionnaires.

scholarly journals Inferring exemplar discriminability in brain representations

2016 ◽  
Author(s):  
Hamed Nili ◽  
Alexander Walther ◽  
Arjen Alink ◽  
Nikolaus Kriegeskorte
Keyword(s):  
Fixed Effects ◽  
Statistical Tests ◽  
Random Effect ◽  
Nonparametric Tests ◽  
Test Statistics ◽  
Brain Response ◽  
Test Statistic ◽  
Mahalanobis Distances ◽  
Linear Discriminant ◽  
Wide Range

AbstractRepresentational distinctions within categories are important in all perceptual modalities and also in cognitive and motor representations. Recent pattern-information studies of brain activity have used condition-rich designs to sample the stimulus space more densely. To test whether brain response patterns discriminate among a set of stimuli (e.g. exemplars within a category) with good sensitivity, we can pool statistical evidence over all pairwise comparisons. A popular test statistic reflecting exemplar information is the exemplar discriminability index (EDI), which is defined as the average of the pattern dissimilarity estimates between different exemplars minus the average of the pattern dissimilarity estimates between repetitions of identical exemplars. The EDI is commonly tested with a t test (H0: population mean EDI = 0) across subjects (subject as random effect). However, it is unclear whether this approach is either valid or optimal. Here we describe a wide range of statistical tests of exemplar discriminability and assess the validity (specificity) and power (sensitivity) of each test. The tests include previously used and novel, parametric and nonparametric tests, which treat subject as a random or fixed effect, and are based on different dissimilarity measures, different test statistics, and different inference procedures. We use simulated and real data to determine which tests are valid and which are most sensitive. The popular across-subject t test of the EDI (typically using correlation distance as the pattern dissimilarity measure) requires the assumption that the EDI is 0-mean normal under H0, which is not strictly true. Reassuringly, our simulations suggest that the test controls the false-positives rate at the nominal level and is thus valid in practice. However, test statistics based on average Mahalanobis distances or average linear-discriminant t values (both accounting for the multivariate error covariance among responses) are substantially more powerful for both random- and fixed-effects inference. We suggest preferred procedures for safely and sensitively detecting subtle pattern differences between exemplars.

scholarly journals Selected Statistical Tests for Median and Their Properties

2017 ◽  
Vol 4 (330) ◽  
Author(s):  
Dorota Pekasiewicz ◽  
Agata Szczukocka
Keyword(s):  
Population Distribution ◽  
Simulation Analysis ◽  
Alternative Hypothesis ◽  
Statistical Tests ◽  
Bootstrap Method ◽  
Nonparametric Tests ◽  
Small Samples ◽  
Test Statistic ◽  
Sample Median ◽  
Critical Regions

In the paper, a selection of statistical tests for median are presented. In particular, parametric and nonparametric significance tests are considered. In the case of parametric tests the critical regions are constructed on the basis of the known population distribution and the form of the alternative hypothesis. For chosen distributions the critical values are presented. In the case of nonparametric tests we consider tests for which the sample median dispersion is estimated based on order statistics of appropriate ranks. The use of the bootstrap method for the median dispersion estimation in the test statistic construction is the author’s own proposal. The simulation analysis of the nonparametric tests’ properties allows to compare these tests with each other, showing better results for the bootstrap variant, especially for small samples.

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

AbstractMotivationPermutation tests offer a straight forward 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 naive 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.ResultsParallelization of the Green algorithm was found possible by nontrivial 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.AvailabilityIn Python 3 code from the GitHub repository https://github.com/statisticalbiotechnology/parallelPermutationTest under an Apache 2.0 [email protected] informationSupplementary data are available at Bioinformatics online.

scholarly journals Inferential, Nonparametric Statistics to Assess the Quality of Probabilistic Forecast Systems

2007 ◽  
Vol 135 (2) ◽  
pp. 351-362 ◽  
Author(s):  
Alinede H. N. Maia ◽  
Holger Meinke ◽  
Sarah Lennox ◽  
Roger Stone
Keyword(s):  
Southern Oscillation ◽  
Statistical Tests ◽  
Quality Measures ◽  
Nonparametric Tests ◽  
P Values ◽  
Skill Scores ◽  
Significance Levels ◽  
Nonparametric Statistical ◽  
Forecast Quality

Abstract Many statistical forecast systems are available to interested users. To be useful for decision making, these systems must be based on evidence of underlying mechanisms. Once causal connections between the mechanism and its statistical manifestation have been firmly established, the forecasts must also provide some quantitative evidence of “quality.” However, the quality of statistical climate forecast systems (forecast quality) is an ill-defined and frequently misunderstood property. Often, providers and users of such forecast systems are unclear about what quality entails and how to measure it, leading to confusion and misinformation. A generic framework is presented that quantifies aspects of forecast quality using an inferential approach to calculate nominal significance levels (p values), which can be obtained either by directly applying nonparametric statistical tests such as Kruskal–Wallis (KW) or Kolmogorov–Smirnov (KS) or by using Monte Carlo methods (in the case of forecast skill scores). Once converted to p values, these forecast quality measures provide a means to objectively evaluate and compare temporal and spatial patterns of forecast quality across datasets and forecast systems. The analysis demonstrates the importance of providing p values rather than adopting some arbitrarily chosen significance levels such as 0.05 or 0.01, which is still common practice. This is illustrated by applying nonparametric tests (such as KW and KS) and skill scoring methods [linear error in the probability space (LEPS) and ranked probability skill score (RPSS)] to the five-phase Southern Oscillation index classification system using historical rainfall data from Australia, South Africa, and India. The selection of quality measures is solely based on their common use and does not constitute endorsement. It is found that nonparametric statistical tests can be adequate proxies for skill measures such as LEPS or RPSS. The framework can be implemented anywhere, regardless of dataset, forecast system, or quality measure. Eventually such inferential evidence should be complemented by descriptive statistical methods in order to fully assist in operational risk management.

scholarly journals How Different Are the Nordics? Unravelling the Willingness to Make Economic Sacrifices for the Environment

2021 ◽  
Vol 13 (3) ◽  
pp. 1294
Author(s):  
Joseph Anthony L. Reyes
Keyword(s):  
Multinomial Logistic Regression ◽  
Statistical Tests ◽  
Empirical Studies ◽  
Environmental Policies ◽  
Social Survey ◽  
Proenvironmental Behavior ◽  
Attitudes And Behaviors ◽  
Nordic Region ◽  
And Behaviors ◽  
Nonparametric Statistical

The Nordic countries are often considered as remarkably exceptional in terms of the proenvironmental behavior of their citizens and also as forerunners in environmental policies. However, very few empirical studies have been done at the aggregated level about how the Nordics compare to other countries. The article addresses this knowledge gap and analyzes the Nordic region in terms of willingness to make economic sacrifices, proenvironmental attitudes and behaviors. Data (N = 5877) from the environment module of the International Social Survey Program (ISSP) are utilized, with nonparametric statistical tests and multinomial logistic regression employed—wherein, emphasis is placed on the regression models for willingness as dependent variables as analysis of the first order, with attitudes, behaviors and sociodemographic variables as part of second order analysis. The findings reveal that the region’s higher levels of willingness, attitudes, and behaviors become more salient when compared to third countries. People in the Nordic region who are ‘neither willing nor unwilling’ to protect the environment can be considered as distinct, and should not be arbitrarily lumped within the categories of the ‘unwilling’ or ‘willing’ respondents. These insights allow for a deeper understanding of peoples’ willingness and the relationships to respective attitudes and behaviors beneficial towards engaging the acceptability of extant environmental policies.

scholarly journals The Effect Of Counseling On The Adherence Of Therapeutic Hypertension Patients

2020 ◽  
Vol 11 (2) ◽  
Author(s):  
Gita Sekar Prihanti ◽  
Novi Puspita Sari ◽  
Nur Indah Septiani ◽  
Laura Putri Risty L. Tobing ◽  
Annisa Rahayu Adrian ◽  
...  
Keyword(s):  
Family Support ◽  
Statistical Tests ◽  
Adherence Rate ◽  
Test Results ◽  
A Value ◽  
Significant Difference ◽  
Post Test ◽  
Lifestyle Education ◽  
Nonparametric Statistical ◽  
Adherence To Therapy

Failure of therapy is a result of bad adherence  medication. Non-adherence to therapy is a major factor that is suspected to result in uncontrolled blood pressure in hypertensive patients resulting in more serious complications. Therefore it is important to increase the adherence rate of treatment in patients with hypertension in the treatment process. For this reason, the need for interventions to improve  adherence  with several aspects that can be changed. This study uses One Group Pretest-Posttest Design using 100 samples. Data derived from questionnaires containing 25 items of adherence to therapy, 5 items of knowledge, 4 items of trust, 3 items of motivation, 10 items of family support with nonparametric statistical tests used were Mc Nemar test. Mc Nemar test results indicate that there is a significant difference between adherence at the pre-test and at the post-test after counseling with a significance value (p = 0,000). The results also showed that there was a difference in knowledge with a significance value (p = 0.001), motivation with a value (p = 0.031) and family support with a value (p = 0,000). The education with counseling about knowledge, trust, motivation and family support is effective in increasing compliance. There are other changeable factors such as lifestyle education, patient doctor relationships, and the use of smartphone applications for self-reported therapy can improve adherence in patients thereby minimizing therapy failure. Other educational methods that can be used besides counseling are counseling and dissemination of social media information.

scholarly journals Some Nonparametric Statistical Tests for Quick Evaluation of Clinical Data

1975 ◽  
Vol 21 (3) ◽  
pp. 309-314 ◽  
Author(s):  
E Melvin Gindler
Keyword(s):  
Control Chart ◽  
Patient Population ◽  
Statistical Tests ◽  
Test Results ◽  
Laboratory Error ◽  
Unusual Distribution ◽  
Run Test ◽  
Nonparametric Statistical ◽  
And Control ◽  
The Given

Abstract Some rapid statistical tests give (a) rapid answers on how well methods agree and control chart evaluation (sign and run tests) and (b) evaluation of distribution of test results (Tukey's quick test and run test). These tests mainly require counting of data and the use of the given nomograms. An unusual distribution of patient test values—that is, unusual when compared with the generally observed distribution of the data seen in a particular laboratory—may indicate laboratory error, alteration of specimens (as from poor collection and/or storage techniques, such as evaporation), or an unusual patient population.

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