在廣義線性複迴歸的架構下，Tsou (2009)對於常態實作模型提出了概似函數的修正法。當樣本數大且資料真正的分配未知的時候，即使模型假設錯誤，仍可對有興趣的迴歸參數提供正確的推論。 使用變異數分析(ANOVA)來檢定統計資料受到那些因素的影響時，必需要假設資料服從常態分配，當真實資料不符合常態分配假設時，引用變異數分析所提供的F統計量來判斷解釋變數是否影響反應變數會造成錯誤的推斷。 本文將此強韌法應用至變異數分析中，進一步修正F統計量與概似比統計量，研究發現，即使真實資料不符合常態分配假設，強韌變異數分析仍可提供迴歸模型正確的統計分析。 Under the generalized multiple linear regression, Tsou(2009) proposed the robust likelihood method for normal working model. Even if the working model is wrong, it still provides correct inferences for the parameter of interest. We focus on applying the robust method to the analysis of variance, and further revising the F statistic and the likelihood ratio statistic. Using the robust F statistic can correctly infer the significance of regressors. The robust analysis of variance can still provide correct statistical analysis for a regression model, even if the normal assumption is improper. The efficacy of the proposed robust method is demonstrated via simulation studies and real data analyses.
