How to compare small multivariate samples using nonparametric tests
How to compare small multivariate samples using nonparametric tests
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DOI：
10.1016/j.csda.2008.04.006
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发表时间：
2008-07-15
影响因子：
1.8
通讯作者：
Madden, Laurence V.
中科院分区：
文献类型：
--
作者：
Bathke, Arne C.;Harrar, Solomon W.;Madden, Laurence V.
在生命科学和其他研究领域，经常进行实验来确定受试者对各种治疗的反应。通常，这样的数据是多变量的，其中不同的变量可以在不同的尺度上测量，可以是定量的、顺序的或混合的。为了分析这些数据，我们对平衡和非平衡单向布局中的多变量观测提出了不同的非参数(基于等级)检验。以前的工作已经导致了基于渐近理论的测试的发展，无论是针对大量的样本还是针对组；然而，大多数实验只包括每个单独的组或样本中的少量或中等数量的实验单元。在这里，我们研究了几种基于小样本近似的测试，并比较了它们在不同模拟情况下的阿尔法水平和功率方面的性能，以及连续和离散观测。对于正相关响应，基于[Brunner，E.，Dette，H.，Munk，A.，1997.非参数析因设计中的箱型逼近。J·阿梅尔。统计学家。阿索克。ANOVA型统计量表现最好；对于负相关的回答，一般来说，基于Lawley-Hotellirg型检验的近似值表现最好。我们演示了在植物病理学实验中基于近似的测试的使用。(C)2008年，爱思唯尔出版。
In the life sciences and other research fields, experiments are often conducted to determine responses of subjects to various treatments. Typically, such data are multivariate, where different variables may be measured on different scales that can be quantitative, ordinal, or mixed. To analyze these data, we present different nonparametric (rank-based) tests for multivariate observations in balanced and unbalanced one-way layouts. Previous work has led to the development of tests based on asymptotic theory, either for large numbers of samples or groups; however, most experiments comprise only small or moderate numbers of experimental units in each individual group or sample. Here, we investigate several tests based on small-sample approximations, and compare their performance in terms of alpha levels and power for different simulated situations, with continuous and discrete observations. For positively correlated responses, an approximation based on [Brunner, E., Dette, H., Munk, A., 1997. Box-type approximations in nonparametric factorial designs. J. Amer. Statist. Assoc. 92, 1494-1502] ANOVA-Type statistic performed best; for responses with negative correlations, in general, an approximation based on the Lawley-Hotellirg type test performed best. We demonstrate the use of the tests based on the approximations for a plant pathology experiment. (C) 2008 Published by Elsevier B.V.