New tests are developed for two-way ANOVA models with heterogeneous error variances. The testing problems are considered for testing the significant interaction effects, simple effects, and treatment effects. The likelihood ratio tests (LRTs) and simultaneous comparison tests are derived for all three problems. Hill climbing algorithms have been proposed to compute the maximum likelihood estimators (MLEs) of parameters under the restrictions on the null and alternative hypotheses. It is proved that the proposed algorithms converge to the MLEs. A parametric bootstrap algorithm is provided for the computation of the critical points. The simulated power values of the proposed tests are compared with two existing tests. For testing main effects in the additive ANOVA model, the LRT appears to be about $30\%$ to $50\%$ gain in power over the available tests. Also, the proposed tests for the interaction and simple effects are seen to have comparable power and size performance to the existing tests. The behavior of the proposed tests under the non-normal error distribution is also discussed. Four real data sets are used to demonstrate the application of the proposed tests. A software package is made in `R' to make it simple to apply the tests to experimental data sets.

翻译：本文针对具有异质误差方差的双向方差分析模型提出了新的检验方法。研究考虑了交互效应、简单效应和处理效应的显著性检验问题。针对这三个问题，推导了似然比检验和同步比较检验。提出了爬山算法以计算零假设和备择假设约束下参数的最大似然估计量，并证明了所提算法能收敛至最大似然估计量。提供了参数自助法算法用于临界值计算。通过模拟实验将所提检验的功效值与两种现有检验方法进行比较。在可加性方差分析模型中检验主效应时，似然比检验相较于现有检验方法显示出约$30\%$至$50\%$的功效提升。同时，所提出的交互效应和简单效应检验在功效和规模性能方面与现有检验方法表现相当。还讨论了非正态误差分布下所提检验的表现特征。通过四个实际数据集展示了所提检验的应用场景，并开发了`R`语言软件包以简化实验数据集的检验流程。