在統計分析上，樣本數決定的主要目的是希望有足夠的樣本，使得在做統計檢定時能達到事先決定的型一誤差機率和檢定力。而在許多分析進行之前，常會先抽一組小樣本，來估計所假設模型中的參數，進而預測所需要的樣本數。但如果假設的模型和真正的資料分配不符時，那麼所決定的樣本數將不正確。因此會使檢定的型一誤差機率和檢定力達不到原先的要求。 Royall & Tsou (2003) 提出強韌概似函數 (robust likelihood function) 的觀念。在樣本數大的時候，即使資料的真正分配未知，強韌概似函數還是能正確提供關於有興趣參數的資訊。而Tsou (2004) 則將上述強韌概似函數的概念推廣到在廣義線性模型之下的迴歸參數推論問題。 本文主要利用強韌迴歸方法來決定樣本數，並比較利用強韌常態模型、強韌伽瑪模型及強韌逆高斯模型時，所需要樣本數大小之間的差異。 In statistical analysis, the capital purpose of determining sample size is to obtain enough sample size in order to achieve the probability of type one error and power. Before analyzing, we usually take a small sample size to estimate parameters in model, then to calculate sample size. But, if the model is wrong, the sample size is incorrect. Thus, the probability of type one error and power will not achieve the goal. Royall & Tsou (2003) brought up robust likelihood function., Even we don’t know the real distribution of data, robust likelihood function will provide correct information of parameters of interest when sample size is large. And Tsou (2004) spread it to general linear model. The paper use the method of robust regression to determine sample size, and compare sample size in robust normal model, robust gamma model and robust inverse Gaussian model.
