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Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

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Nội dung chi tiết: Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

Comparison of nonparametric analysis of variance methods a Monte Carlo studyPart A: Between subjects designs - A Vote for van der WaerdenVersion 4.1 c

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham sốcompletely revised and extended (15.8.2016)Haiko LOpsenRegionales Rechenzentrum (RRZK)Kontakt: Luepsen@Uni-Koeln.deUniversităt ZU KolnIntroductionComp

arison of nonparametric analysis of variance methods - a Vote for van der WaerdenAbstractFor two-way layouts in a between subjects anova design the pa Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

rametric F-test is compared with seven nonparametric methods: rank transform (RT), inverse normal transform (INT), aligned rank transform (ART), a com

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

bination of ART and INT, Puri & Sen's L statistic, van der Waerden and Akritas & Brunners ATS. The type I error rates and the power are computed for 1

Comparison of nonparametric analysis of variance methods a Monte Carlo studyPart A: Between subjects designs - A Vote for van der WaerdenVersion 4.1 c

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham sốluding the null and the full model. The aim of this study is to identify a method that is applicable without too much testing all the attributes OÍ' t

he plot. The van der Waerden-test shows the overall best performance though there are some situations in which it is disappointing. The Puri & Sen- an Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

d the ATS-tests show generally a very low power. These two as well as the other methods cannot keep the type I error rate under control in too many si

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

tuations. Especially in the case of lognormal distributions the use of any of the rank based procedures can be dangerous for cell sizes above 10. As a

Comparison of nonparametric analysis of variance methods a Monte Carlo studyPart A: Between subjects designs - A Vote for van der WaerdenVersion 4.1 c

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số. And heterogeneity of variances leads to an inflated error rate more or less also for the nonparametric methods. Finally it should be noted that some

procedures, e.g. the ART, show poor surprises with increasing cell sizes, especially for discrete variables.Ă.'ẹn»-ords: nonparametric anova. rank tr Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

ansform. Puri & Sen. ATS. Waerden, simulation1. IntroductionThe analysis of variance (anova) is one of the most important and frequently used methods

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

of applied statistics. In general it is used in its parametric version often without checking the assumptions. These are normality of the residuals, h

Comparison of nonparametric analysis of variance methods a Monte Carlo studyPart A: Between subjects designs - A Vote for van der WaerdenVersion 4.1 c

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham sốtrust in the robustness of the parametric tests. .A test is called robust when Us significance level (Type I error probability) and power (one minus T

ype-II probability') are insensitive to departures from the assumptions on which it is derives.** (See Ito. 1980). Good reviews of the assumptions and Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

the robustness can be found at Field (2009). Bortz (1984)and Ito (1980). more detailed descriptions at Fan (2006). Wilcox (2005), Osborne (2008). Lin

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

dman (1974) as well as Glass, Peckham & Sanders (1972). They state that first the F-test is remarkable insensitive to general nonnormality, and second

Comparison of nonparametric analysis of variance methods a Monte Carlo studyPart A: Between subjects designs - A Vote for van der WaerdenVersion 4.1 c

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham sốarticles by Box (1954) and Glass et al. (1972) who report that even in balanced designs unequal variances may lead to an increased type I error rate.

Nevertheless there may exist other methods which are superior in these cases even when the F-test may be applicable. Furthermore dependent variables w Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

ith an ordinal scale normally require adequate methods.The knowledge of nonparametric methods for the anova is not wide spread though in recent years

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

quite a number of publications on this topic appeared. Salazar-Alvarez et al. (2014) gave a review of the most recognized methods. Another easy to rea

Comparison of nonparametric analysis of variance methods a Monte Carlo studyPart A: Between subjects designs - A Vote for van der WaerdenVersion 4.1 c

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham sốall the information in the data. This is not true.Methods to be comparedSawilowsky (1990) also showed that most well known nonparametric procedures, e

specially those considered here, have a power comparable to their parametric counterparts, and often a higher power when assumptions for the parametri Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

c tests are not met.On the other side are nonparametric methods not always acceptable substitutes for parametric methods such as the F-test in researc

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

h studies when parametric assumptions are not satisfied. ,Jt came to be widely believed that nonparametric methods always protect the desired signific

Comparison of nonparametric analysis of variance methods a Monte Carlo studyPart A: Between subjects designs - A Vote for van der WaerdenVersion 4.1 c

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham sốriance (anova) with the assumptions of normality and variance homogeneity. And there exist a number of studies showing that nonparametric procedures c

annot handle skewed distributions in the case of heteroscedasticity (see e.g. G. Vallejo et al.. 2010. Kesehnan et al., 1995 and Tomarken & Serlin. 19 Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

86).A barrier for the use of nonparametric anova is apparently the lack of procedures in the statistical packages, e.g. SAS and SPSS though there exis

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

t some SAS macros meanwhile. Only for R and S-Plus packages with corresponding algorithms have been supplied during the last two years. But as is show

Comparison of nonparametric analysis of variance methods a Monte Carlo studyPart A: Between subjects designs - A Vote for van der WaerdenVersion 4.1 c

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham sốt of programming, for instance to do some variable transformations. For. a number of nonparametric methods can be applied by transforming the dependen

t variable. Such algorithms stay in the foreground.The aim of this study is to identify situations, e.g. designs or underlying distributions, in which Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

one method is superior compared to others. For. many appliers of the anova know only little of their data, the shape of the distribution, the homogen

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

eity of the variances or expected size of the effects. So. overall good performing methods are looked for. But attention is also laid upon comparisons

Comparison of nonparametric analysis of variance methods a Monte Carlo studyPart A: Between subjects designs - A Vote for van der WaerdenVersion 4.1 c

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham sốerent levels of effect or sample size. Here the focus is laid not only upon the tests for the interaction effects but also on the main effects as the

properties of the tests have not been studied exhaustively in factorial designs. Additionally the behavior of the type I error rates is examined for i Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

ncreasing cell sizes up to 50, because fu st, as a consequence of the central limit theorem some error rates should decrease for larger nt. and second

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

most nonparametric tests are asymptotic.The present study is concerned only with between subjects designs. Because of the large amount of resulting m

Comparison of nonparametric analysis of variance methods a Monte Carlo studyPart A: Between subjects designs - A Vote for van der WaerdenVersion 4.1 c

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham sốers.2. Methods to be comparedIt follows a brief description of the methods compared in this paper. More information, especially how to use them in R o

r SPSS can be found in Luepsen (2015).The anova model shall be denoted byxyk =+with fixed effects oq (factor A), |5j (factor B). (Zpjj (interaction AB Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

) and error Cjj-f..Methods to be compared32. 1 RT (rank transform)The rank transform method (RT) is just transforming the dependent variable (dv) into

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

ranks and then applying the parametric anova to them. This method had been proposed by Conover & Iman (1981). Blair et al. (1987), Toothaker & Newman

Comparison of nonparametric analysis of variance methods a Monte Carlo studyPart A: Between subjects designs - A Vote for van der WaerdenVersion 4.1 c

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham sốvel if there are significant main effects because the effects are confounded. On the other hand the RT lets sometimes vanish an interaction effect, as

Salter & Fawcett < 1993) had shown in a simple example. The reason: „ additivity’ in the raw data does not imply additivity of the ranks, nor does ad Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

ditivity of the ranks imply additivity in the raw data", as Hora & Conover (1984 ) pointed out. At least Hora & Conover (1984 ) proved that the tests

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

of the main effects are correct. A good review of articles concerning the problems of the RT can be found in the study by Toothaker & Newman (1994).2.

Comparison of nonparametric analysis of variance methods a Monte Carlo studyPart A: Between subjects designs - A Vote for van der WaerdenVersion 4.1 c

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham sốn computing their normal scores and finally applying the parametric ano-va to them. The normal scores are defined as

ks of the dv and n is the number of observations. It should be noted that there exist several versions of the normal scores (see Beasley. Erickson & A Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

llison (2009) for details). This results in an improvement of the RT procedure as could be shown by Huang (2007) as well as Mansouri and Chang (1995).

Comparison of nonparametric analysis of variance methods So sánh các phương pháp phân tích phương sai phi tham số

though Beasley. Erickson & Allison (2009) found out that also the INT procedure results in slightly too high type I eiTor rates if there are other si

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