摘要
在應用科學中，效果量被廣泛的使用在估計平均數的大小， 效果量已經被20多種期刊所重視，而且有迅速增加的趨勢，不論在各式各樣的研究裡，作者都會被要求附上效果量的估計值， 舉個例子， Wilkinson (1999) 在APAfootnote{Wilkinson & American Psychological Association Task Force on Statistical Inference, 1999, p.599}期刊中強調 "總是為這些重要的結果附上效果量dots，在實用且理論的文章中，這些效果量將有助於結果增加ㄧ些解釋dots"。 在這篇論文中，我們用迴歸分析的方法和基本的定義來推導計算效果量，並且發展出一套效果量和自變數間關係的線性模型理論結構， 這篇論文有三個重點: egin{enumerate} item 效果量的不偏估計量 item 效果量的一致最小變異不偏估計量 item 效果量的一般線性假設檢定。 end{enumerate} 我們簡潔地介紹一下這篇論文， 假設應變數 $y$ 是一個單變量的常態分布且效果量為 $ oldsymbol{ eta'x}$， 利用最大概似法求得效果量的最大概似估計量， 再將效果量的估計量取期望值就可以得到效果量的不偏估計量， 為了得到效果量的一致最小變異不偏估計量，我們只要找到ㄧ個估計量為效果量的完備充份統計量而且不偏， 再根據Rao-Blackwell-Lehmann-Scheff$acute{ extrm{e}}$定理，這個估計量就是效果量的一致最小變異不偏估計量， 在假設檢定中，為效果量定義一個檢定統計量和信賴區間， 最後，我們將會用真實的資料解釋我們的研究結果。
並列摘要
Effect size is widely used as a measure of the magnitude of mean in applied science. Emphasis on effect sizes is a rapidly rising tide as over 20 journals in various fields of research now require that authors reports provide estimates of effect size. For example, the American Psychological Association (APA) Task Force on Statistical Inference recently emphasized, "Always present effect size for primary outcomesdots. It helps to add brief comment that place these effect sizes in a practical and theoretical contextdots" (Wilkinson & APA Task Force on Statistical Inference, 1999, p.599). In this article, we make inference and calculate effect sizes in regression method using a ubiquitous definition, and develop the theoretical framework of linear model between effect size and independent variables. This article have three focal points: egin{enumerate} item unbiased estimation of effect sizes item UMVUE for effect sizes item general linear hypothesis test for effect sizes. end{enumerate} We introduce this article pithily. Suppose that dependent variable $y$ is univariate normal distribution and effect size is $ oldsymbol{ eta'x}$. Using maximum likelihood method, we can find an estimator of effect size. As for the unbiased estimation of effect size, it can be obtained by taking expertation on the estimator of effect size. For obtaining UMVUE of effect size, it suffices to find an estimator of effect size which is a complete sufficient statistic and an unbiased estimator for effect size. Thus the estimator is a UMVUE for effect size according to Rao-Blackwell-Lehmann-Scheff$acute{ extrm{e}}$ theorem. In general linear hypothesis test, we define a test statistic and a confidence interval for effect size. At last, we illustrate these results of our study with real data.