A comparison of the power of the <i>t</i> test, Wilcoxon's test, and the approximate permutation test for the two‐sample location problem

Brink, Wulfert P. van den; Brink, Sebastiaan G. J. van den

doi:10.1111/j.2044-8317.1989.tb00907.x

Cited by 28 publications

(3 citation statements)

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“…Others show that t -tests may lose power when normality is violated (e.g. Blair & Higgins, 1980a, 1980b, 1981, 1985van den Brink & van den Brink, 1989). Wilcox (2001Wilcox ( , 2022 demonstrated numerous examples of the vulnerability of parametric tests to subtle violations of distributional assumptions.…”

Section: Normality and T -Testsmentioning

confidence: 99%

“…Islam (2017) found the Anderson-Darling test to have the highest power for all sample sizes on the complete selected class of alternatives, followed closely by the Chen-Shapiro (Chen & Shapiro, 1995) test, which performs particularly well with smaller and medium sample sizes. Numerous reviews of univariate goodness-of-fit (GOF) normality tests have been published (e.g., Adefisoye et al, 2016;Ahmad & Sherwani, 2015;Arnastauskaitė et al, 2021;Islam, 2017Islam, , 2019Farrell & Rogers-Stewart, 2006;Pedrosa et al, 2015;Romāo et al, 2010;Seier, 2002;Sürücü, 2008;Schick et al, 2011;Uyanto, 2022;Yap & Sim, 2011;Wijekularathna et al, 2022). With the exception of Adefisoye et al (2016), Arnastauskaitė et al (2021), Romāo et al (2010), and Uyanto ( 2022), most reviews have covered only a small number of well-known tests or focused on a specific class of tests, such as the entropy-based estimators (e.g., Alizadeh Noughabi & Arghami, 2011, 2012Zamanzade & Arghami, 2012).…”

Section: How Should Researchers Evaluate the Normality Assumption?mentioning

confidence: 99%

“…Quessy and Mailhot (2011) suggest four kinds of alternative distributions; namely, bimodal alternatives, kurtosis alternatives, heavy-tailed alternatives, and mixture of skewness and kurtosis alternatives. Alizadeh Arghami (2011, 2012), Uyanto (2022) and Zamanzade and Arghami (2012) categorize distributions into four categories; namely, symmetric distributions with support for (−∞, ∞), asymmetric distributions with support for (−∞, ∞), distributions with support bounded at (0, ∞), and distributions with support bounded at (0, 1). The greatest number of categories was defined by Seier (2002), who used a total of 9 categories.…”

Section: Population Distributions Included In This Studymentioning

confidence: 99%

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Managing the Assumption of Normality within the General Linear Model with Small Samples: Guidelines for Researchers Regarding If, When and How.

Zygmont

2023

TQMP

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Academic textbooks, statistical literature, and publication guidelines provide conflicting, ambiguous and often incomplete answers to the question of how researchers should handle the normality assumption for classical general linear model tests when conducting their analyses. Previous studies have shown that normality violations can impact on type I errors, power, parameter estimates and standard error estimates of classical tests. This paper reviews the arguments in favour and against normality testing, the role of the central limit theorem, types of violations that tests within the general linear model are susceptible to, methods for evaluating the normality assumption, and the paradox that normality tests have low power in small sample sizes where the influence of assumption violations are likely to be most profound. A Monte Carlo simulation study was used to evaluate the power of 18 normality tests across 18 alternative distributions, and the effect of normality deviations on estimates of centrality, scatter and regression coefficients. The results demonstrate that the type of normality test and distribution matters, and that a conditional testing procedure utilising normality tests to select between classic, non-parametric and robust tests should not be used. Instead, an alternative procedure for managing the normality assumption is advised, and demonstrated in the supplementary materials using R code and data that are provided.

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Section: Normality and T -Testsmentioning

confidence: 99%

Section: How Should Researchers Evaluate the Normality Assumption?mentioning

confidence: 99%

Section: Population Distributions Included In This Studymentioning

confidence: 99%

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Managing the Assumption of Normality within the General Linear Model with Small Samples: Guidelines for Researchers Regarding If, When and How.

Zygmont

2023

TQMP

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Efficiency comparisons of rank and permutation tests by Phillip I. Good Statistics in Medicine 2004; 23:857

Neuhäuser¹

2005

Statistics in Medicine

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In a recent letter, Good [1] wrote that rank tests have a lower ARE than permutation tests that use the original observations. As a consequence, Good [1] recommended rank tests for two cases only. To be precise, the use of ranks was recommended when outliers are a concern or when combining results measured with di erent precision.Let us consider the comparison of two samples. Contaminated distributions are fairly common in certain areas of research [7]. Such a mixture may be a suitable model in the presence of outliers. Furthermore, outliers can lead to heavy-tailed distributions [8]. However, the Wilcoxon test is much more powerful than the Fisher-Pitman test also for a common asymmetric distribution such as 2 [5]. In summary, the Wilcoxon test can be much more powerful than the Fisher-Pitman test under non-normality. In contrast, the Fisher-Pitman test shows only a modest power advantage over the Wilcoxon test for the normal distribution [5]. Therefore, the Wilcoxon test is a good choice when the underlying distribution function is a priori unknown as it usually is in practice. Hence, permutation tests on ranks are still useful despite the fact that more complicated permutation tests can easily be carried out nowadays.

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Testing related samples with missing values: a permutation approach

Mundry

1999

Animal Behaviour

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A comparison of the power of the t test, Wilcoxon's test, and the approximate permutation test for the two‐sample location problem

Cited by 28 publications

References 6 publications

Managing the Assumption of Normality within the General Linear Model with Small Samples: Guidelines for Researchers Regarding If, When and How.

Managing the Assumption of Normality within the General Linear Model with Small Samples: Guidelines for Researchers Regarding If, When and How.

Efficiency comparisons of rank and permutation tests by Phillip I. Good Statistics in Medicine 2004; 23:857

Testing related samples with missing values: a permutation approach

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