Permutation tests of scale using deviances

Richter, Scott J.; McCann, Melinda H.

doi:10.1080/03610918.2016.1165844

Cited by 5 publications

(2 citation statements)

References 18 publications

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“…This test will be referred to as the RMD test. The RMD test was found [14] to be generally superior to W50 and OB, although there were still cases where each of W50 and OB had higher power. Since no test has been found to be uniformly superior, it is of interest to develop a test that combines these three tests.…”

Section: Introductionmentioning

confidence: 87%

Combined Permutation Tests for Pairwise Comparison of Scale Parameters Using Deviances

Richter,

McCann

2024

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Nonparametric combinations of permutation tests for pairwise comparison of scale parameters, based on deviances, are examined. Permutation tests for comparing two or more groups based on the ratio of deviances have been investigated, and a procedure based on Higgins’ RMD statistic was found to perform well, but two other tests were sometimes more powerful. Thus, combinations of these tests are investigated. A simulation study shows a combined test can be more powerful than any single test.

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Section: Introductionmentioning

confidence: 87%

Combined Permutation Tests for Pairwise Comparison of Scale Parameters Using Deviances

Richter,

McCann

2024

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“…Thus, we propose to perform two further tests, one on the median differences and another on the scale differences. The scale test is a test on the deviance from the median [26]. We do them on the median, as opposed to the mean, in order to perform non-parametric robust tests.…”

Section: Tests On the Statistical Depth Valuesmentioning

confidence: 99%

Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients

2021

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Black-box techniques have been applied with outstanding results to classify, in a supervised manner, the movement patterns of Alzheimer’s patients according to their stage of the disease. However, these techniques do not provide information on the difference of the patterns among the stages. We make use of functional data analysis to provide insight on the nature of these differences. In particular, we calculate the center of symmetry of the underlying distribution at each stage and use it to compute the functional depth of the movements of each patient. This results in an ordering of the data to which we apply nonparametric permutation tests to check on the differences in the distribution, median and deviance from the median. We consistently obtain that the movement pattern at each stage is significantly different to that of the prior and posterior stage in terms of the deviance from the median applied to the depth. The approach is validated by simulation.

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Pairwise comparison of scale using deviances

Richter

McCann

2019

Journal of Statistical Computation and Simulation

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Keselman et al. [8], Conover et al. [9], and Balakrishnan and Ma [10]. O'Brien [11] proposed a modification of Levene's test (OB50) which has been recommended over the W50 test for lighter-tailed distributions [11,12]. Marozzi [13] considered the W50 and OB50 tests, as well as permutation versions of these tests, and found that the permutation versions of these tests tended to be more robust and have higher power. They recommended the permutation W50 test as a computationally simple robust test, but also the permutation version of OB50, which had higher power for symmetric and lighter-tailed skewed distributions. Richter and McCann [14] found that the permutation RMD test due to Higgins [15] was generally superior to W50 and OB50, especially for heavier-tailed distributions. In this paper, we extend the RMD, W50 and OB50 tests to the problem of simultaneous pairwise comparison of scale. The method of Richter and McCann [16] is used to control the familywise error rate (FWER), and estimated Type I error rates and power of the methods are compared. 2. Methods Consider a one-way layout with t treatments and observations per treatment. We assume a location-scale model, = + , = 1, … , , = 1, … , where and are the location and scale parameters, respectively, of treatment i, and are independent and identically distributed with median 0. It is desired to test 0 ∶ = versus ∶ = for all pairs ≠. 2.1. LEV and W50 tests Levene [6] proposed a robust test (LEV) to compare scale parameters, using the ANOVA Fstatistic computed on the absolute deviations from the treatment means, = � − �. Brown and Forsythe [7] suggested a statistic (W50) that instead used absolute deviations from the treatment medians, = � − �, which we will refer to in the remainder of the paper as deviances. Conover et al. [9] found W50 to have better power and size properties than LEV. Both Levene [6] and Brown and Forsythe [7] suggested that p-values be based on the Fdistribution with − 1 and − degrees of freedom. Marrozzi [13], however, examined permutation versions of these tests, and found the permutation versions to be more robust and more powerful than those based on the F-distribution. 2.2. OB50 tests O'Brien [11] proposed a modification to LEV, suggesting the scores () =

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Permutation tests of scale using deviances

Cited by 5 publications

References 18 publications

Combined Permutation Tests for Pairwise Comparison of Scale Parameters Using Deviances

Combined Permutation Tests for Pairwise Comparison of Scale Parameters Using Deviances

Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients

Pairwise comparison of scale using deviances

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