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首页> 外文期刊>Decision Science Letters >The comparison of nonparametric statistical tests for interaction effects in factorial design
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The comparison of nonparametric statistical tests for interaction effects in factorial design

机译：因子设计中交互作用的非参数统计检验的比较

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Correct application of the classical factorial F-test depends on normality and homogeneity of variance assumptions. If these assumptions are violated the type I error rate will be inflated and power of the test will be decreased. Therefore nonparametric statistical tests have been proposed to analyze the interaction effects in factorial designs. A simulation was conducted to investigate the effect of non-normality on type I error rate and power of the test of the classical factorial F-test and five nonparametric tests namely rank transformation (FR), Winsorized mean (FW), modifies mean (FM), adjusted rank transform (ART) and adjusted median transform (AMT) using program SAS 9.4 with 1,000 replications. The study used 2×2 factorial design with replications of 3, 4 and 6 making sample sizes of 12, 16, and 24, respectively and 3×3 factorial designs with replication of 3 making a sample size of 27 studied at 0.05 level of significance. As a results, when the normality of assumption is satisfied all six statistical tests have the ability to control type I error in all situations. The ART test cannot control type I error rate for 3×3 factorial design when sample size is 27 when normality assumption is violated. For power of the test, the F-test provided the highest test power when the normality of assumption is met. The ART and AMT tests provided approximately the same test power. The AMT and ART tests can be effectively used to analyse the interaction effect between factors A and B in 2×2 factorial design when the sample size is 12 and 16 or 24 respectively and the normality of assumption is not met. Moreover, the results showed that when sample sizes increased, all six statistical tests tended to increase the power of the test.
机译：经典阶乘F检验的正确应用取决于方差假设的正态性和同质性。如果违反了这些假设，则I型错误率将被夸大，测试的功效将降低。因此，已经提出了非参数统计检验来分析析因设计中的交互作用。进行了仿真，以研究非正态性对I型错误率和经典阶乘F检验的功效的影响，以及五个非参数检验，即秩变换（FR），Winsorized均值（FW），修正均值（FM） ），调整后的秩变换（ART）和调整后的中位数变换（AMT），使用程序SAS 9.4进行了1000次复制。该研究使用2×2析因设计，分别重复3、4和6，使样本大小分别为12、16和24;以及3×3析因设计，进行重复3，使得样本大小为27，研究的显着性水平为0.05 。结果，当满足假设的正态性时，所有六个统计检验都具有在所有情况下控制I型错误的能力。当违反正态性假设的样本大小为27时，ART测试无法控制3×3析因设计的I型错误率。对于检验的功效，当满足假设的常态性时，F检验会提供最高的检验功效。 ART和AMT测试提供大约相同的测试功率。当样本量分别为12和16或24且不满足假设的正态性时，AMT和ART测试可以有效地用于分析2×2因子设计中因子A和因子B之间的相互作用。此外，结果表明，当样本数量增加时，所有六个统计检验都倾向于增加检验的功效。

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