An Algorithm for Computing the Exact Distribution of the Kruskal–Wallis Test

Choi, Won Chang; Lee, Jae Won; Huh, Myung Hoe; Kang, Seung Ho

doi:10.1081/sac-120023876

Cited by 15 publications

(7 citation statements)

References 5 publications

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“…Notice that the inequalities (5) are much tighter than those given by Choi et al (2003). Due to this improvement, it would be interesting and desirable to prove the following conjecture.…”

Section: Counting the Number Of Possible Data Setsmentioning

confidence: 99%

“…However, it has been observed in Choi et al (2003) and MacMahon (1979) that it is unlikely that such a formula exists.…”

Section: Formula For C(m N)mentioning

confidence: 99%

“…However, for small cases such as m = 3 and m = 4, the exact distribution of the Kruskal-Wallis statistic has been discussed in the literature (see Choi et al, 2003 andIman et al, 2975).…”

Section: Continuity Correctionmentioning

confidence: 99%

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Combinatorics and Statistical Issues Related to the Kruskal–Wallis Statistic

Bargagliotti

Greenwell

2014

Communications in Statistics - Simulation and Computation

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We explore criteria that data must meet in order for the Kruskal-Wallis test to reject the null hypothesis by computing the number of unique ranked 1 data sets in the balanced case where each of the m alternatives has n observations. We show that the Kruskal-Wallis test tends to be conservative in rejecting the null hypothesis, and we offer a correction that improves its performance. We then compute the number of possible data sets producing unique rank-sums. The most commonly occurring data lead to an uncommonly small set of possible rank-sums. We extend prior findings about rowand column-ordered data structures.

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“…Notice that the inequalities (5) are much tighter than those given by Choi et al (2003). Due to this improvement, it would be interesting and desirable to prove the following conjecture.…”

Section: Counting the Number Of Possible Data Setsmentioning

confidence: 99%

“…However, it has been observed in Choi et al (2003) and MacMahon (1979) that it is unlikely that such a formula exists.…”

Section: Formula For C(m N)mentioning

confidence: 99%

See 1 more Smart Citation

Combinatorics and Statistical Issues Related to the Kruskal–Wallis Statistic

Bargagliotti

Greenwell

2014

Communications in Statistics - Simulation and Computation

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“…Although the Kruskal-Wallis (KW) test is applied when homoscedasticity is deemed suspicious,1 this test is less powerful than the F -test, since it discretises original data using ranks, a sequence of natural numbers such as 1, 2 and 3 to represent ordinal differences in the original continuous outcomes. An even more serious problem with the KW test is its extremely complex distribution of the test statistic and consequently limited applications in practice 2…”

Section: Introductionmentioning

confidence: 99%

Homoscedasticity: an overlooked critical assumption for linear regression

Yang

Chen

2019

Gen Psych

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Linear regression is widely used in biomedical and psychosocial research. A critical assumption that is often overlooked is homoscedasticity. Unlike normality, the other assumption on data distribution, homoscedasticity is often taken for granted when fitting linear regression models. However, contrary to popular belief, this assumption actually has a bigger impact on validity of linear regression results than normality. In this report, we use Monte Carlo simulation studies to investigate and compare their effects on validity of inference.

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“…The higher the occurrence rate is, the more possible the part is defective, namely defective position [6].…”

Section: Assembly Process Of Gearbox Quality Problem Partsmentioning

confidence: 99%

Tracing Method of Quality Issues of Gearbox and Application of Rank Sum Test

Hong¹,

Li²

2016

Advances in Computer Science Research

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Abstract-Tracing quality issues of complex automobile gearbox is realized, defective parts and assembly procedures are analyzed and confirmed, analytical method for tracing quality issues is provided and the thinking is illustrated. Furthermore, the tracing model for assembly and quality issues of the gearbox is constructed based on inference principles of the rank sum test; the research results show that the analytical method is effective and feasible in tracing quality issues of the gearbox.

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An Algorithm for Computing the Exact Distribution of the Kruskal–Wallis Test

Cited by 15 publications

References 5 publications

Combinatorics and Statistical Issues Related to the Kruskal–Wallis Statistic

Combinatorics and Statistical Issues Related to the Kruskal–Wallis Statistic

Homoscedasticity: an overlooked critical assumption for linear regression

Tracing Method of Quality Issues of Gearbox and Application of Rank Sum Test

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