Alver Sarah, Zhang Guoyi
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM, USA.
J Appl Stat. 2023 Aug 9;51(10):1861-1877. doi: 10.1080/02664763.2023.2245179. eCollection 2024.
In one-way analysis of variance models, performing simultaneous multiple comparisons of treatment groups with a control group may be of interest. Dunnett's test is used to test such differences and assumes equal variances of the response variable for each group. This assumption is not always met even after transformation. A parametric bootstrap (PB) method is developed here for comparing multiple treatment group means against the control group with unequal variances and unbalanced data. In simulation studies, the proposed method outperformed Dunnett's test in controlling the type I error under various settings, particularly when data have heteroscedastic variance and unbalanced design. Simulations show that power is often lower for the PB method than for Dunnett's test under equal variance, balanced data, or smaller sample size, but similar to or higher than for Dunnett's test with unequal variance, unbalanced data and larger sample size. The method is applied to a dataset concerning isotope levels found in elephant tusks from various geographical areas. These data have very unbalanced group sizes and unequal variances. This example illustrates that the PB method is easy to implement and avoids the need for transforming data to meet the equal variance assumption, simplifying interpretation of results.
在单向方差分析模型中，对治疗组与对照组进行同时的多重比较可能是有意义的。邓尼特检验用于检验此类差异，并假定每组响应变量的方差相等。即使经过变换，这一假设也并非总能满足。本文开发了一种参数自助法（PB），用于在方差不等和数据不平衡的情况下，将多个治疗组的均值与对照组进行比较。在模拟研究中，所提出的方法在各种设置下控制第一类错误方面优于邓尼特检验，特别是当数据具有异方差和不平衡设计时。模拟表明，在方差相等、数据平衡或样本量较小时，PB方法的功效通常低于邓尼特检验，但在方差不等、数据不平衡和样本量较大时，其功效与邓尼特检验相似或更高。该方法应用于一个关于不同地理区域象牙中同位素水平的数据集。这些数据的组大小非常不平衡且方差不等。这个例子说明，PB方法易于实施，并且无需对数据进行变换以满足方差相等的假设，从而简化了结果的解释。
