Papers and R packages

R package: Parametric Bootstrap Approach for ANOVA models under Unequal Variances with Unbalanced data

Package 'pbANOVA' source code and reference manual

R package 'pbANOVA' is based on Alver and Zhang (2022a, 2022b). The package contains Parametric Bootstrap (PB) procedures for a three-way Analysis of Variance (ANOVA) model without equal variance assumption. It also contains PB procedures for one-way ANOVA models and a PB method for comparing multiple treatment group means against the control group.

For ANOVA models, the traditional F test and Tukey's multiple comparison tests assume equal variance assumption. Krishnamoorthy, Lu, & Mathew, (2007) proposed a PB approach for testing the main factor effect of one-way ANOVA under unequal variances with unbalanced data. Yigit and Gokpinar (2010) carried out a simulation study that investigated performance of the F, W (Welch, 1951), SS (Scott & Smith, 1971), BF (Brown & Forsythe, 1974), Chen-Chen's One Stage (OS) (Chen & Chen, 1998), Chen-Chen's One Stage Range (OSR) (Chen, 2001), Weerahandi's Generalized F (GF) (Weerahandi, 1995), Xu-Wang's Generalized F (XW) (Xu & Wang,2007(a), 2007(b)) and PB tests (Krishnamoorthy et al., 2007). The authors compared Type I error rates and powers of the tests under various settings. PB test is shown to be one of the best for testing the equality of factor level means (overall mean test) under the assumption of heteroscedastic variances. Xu, Yang, Abula, Qin(2013) extended PB overall mean test to two-way ANOVA models.

Another problem in ANOVA is multiple comparison procedures (MCP), i.e., pairwise simultaneous comparisons for all factor levels. Zhang (2015a, 2015b) extended PB approach to MCPs for one-way and two-way ANOVA with unequal group variances and showed that they worked well. Zhang, Christensen, Pesko(2021) examined the relationship between PB and objective Bayesian (OB) approaches for overall mean test of heteroscedastic one-way ANOVA problem. The authors showed that PB and OB overall mean tests for one-way heteroscedastic ANOVA are asymptotically equivalent. Alver and Zhang (2022a) developed the PB procedures for overall test and MCP of a three-way ANOVA model with unequal group variances. Alver and Zhang (2022b) developed a PB method for comparing multiple treatment group means against the control group when the constant variance assumption is violated and data is unbalanced. Simulation studies show that the proposed method outperforms Dunnett's test in controlling the type I error under various settings, particularly when data is with heteroscedastic variance and with unbalanced design.