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A Monte Carlo Simulation Study for Comparing Power of the Most Powerful and Regular Bivariate Normality Tests

机译:蒙特卡洛模拟研究,用于比较最有效和最规则的二元正态性检验的功效

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In many areas of medical research, a bivariate analysis is desirable because it simultaneously tests two correlated response variables. Several parametric bivariate procedures are available but each of them requires bivariate normality assumption for response variables. Although in recent years, continuous efforts have been made to test bivariate normality but it is not clear that which test is the most powerful in specified situation. The aim of this study is to compare power of eight different test of bivariate normality with at least one paper which marked them as a powerful test and dedicate the most powerful test in the specified situation. In this study, power of Mardia skewness, Mardia kurtosis, Henze-Zirkler, Mshapiro, Shapiro-wilk, Royston’s W, Doornik-Hansen and Szekely-Rizzo compared with each other using Monte Carlo simulation techniques. The power study shows that the most powerful test under bivariate distributions with different shapes is not the same. Using simulation studies, we show that “Mshapiro” test will perform much better under symmetric, skewed, medium tailed and heavy tailed distributions. Also, “Royston’s W” test will perform much better when underlying distribution is highly skewed.
机译:在医学研究的许多领域,双变量分析是可取的,因为它可以同时测试两个相关的响应变量。可以使用几种参数双变量过程,但是每个过程都需要对响应变量使用双变量正态性假设。尽管近年来,人们一直在努力测试双变量正态性,但是尚不清楚在特定情况下哪种测试最有效。这项研究的目的是将八项不同的双变量正态性检验的功效与至少一篇论文进行比较,该论文将它们标记为有力检验,并在指定情况下奉献最有力的检验。在这项研究中,使用蒙特卡洛模拟技术将Mardia偏度,Mardia峰度,Henze-Zirkler,Mshapiro,Shapiro-wilk,Royston's W,Doornik-Hansen和Szekely-Rizzo的功效进行了比较。功效研究表明,在具有不同形状的双变量分布下,最有效的检验并不相同。通过仿真研究,我们表明“ Mshapiro”测试在对称,偏斜,中尾和重尾分布下的性能会更好。另外,如果基础分布严重偏斜,“ Royston’s W”测试的性能会更好。

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