結構方程模式的檢定力分析與樣本數決定

Determination of Sample Size and Power Analysis in Structure Equation Modeling

邱皓政(Hawjeng Chiou)

《αβγ量化研究學刊》 2卷1期 (2008/12) Pp. 139-173

摘要

統計檢定力(Power)攸關一個研究是否能夠正確有效的推翻虛無假設，其中牽涉到樣本數的多寡與效果量的大小，因此檢定力分析是用來診斷樣本規模是否適切的重要策略。尤其是在結構方程模式(SEM)，一個模型的優劣好壞除了倚賴模式適配的假設考驗，個別參數的顯著性也與檢定力有密切關係。本文主要即在探討SEM分析當中的檢定力問題，並應用檢定力分析於最小樣本的決定之上。在模式適配部分，除了分就精確適配、接近適配、非接近適配的觀念加以討論之外，並對各種策略提供範例來說明檢定力分析與樣本數決定。從實證數據可以看出，樣本數決定在不同的適配檢驗策略中，各有不同的消長高低，使得樣本數決定必須基於研究者的需要與資料特徵等多方面來考量。至於參數檢定力分析則基於模型當中的不同類型與不同數量的參數有關，在樣本數決定上，必須對於周邊參數與焦點參數分別進行推估，過程相對繁複。本文除了原理討論與範例說明，並提供重要的檢定力分析與樣本數決定對照表，使得相關決策可以快速的利用查表法來進行。文末作者針對檢定力考驗的展望與其他模式分析應用提出討論。

關鍵字

統計檢定力 ； 樣本數規劃 ； 非中央性參數 ； 假設考驗

並列摘要

Statistical power refers to the ability for rejecting a false null hypothesis in hypothesis testing. The power of a study, and required sample size to achieve that power, are very important issues particularly for research using structural equation modeling. As the preliminary requirement of goodness-of-fit of a model, the power analyses in SEM involves in hypothesis testing for model fit, as well as for various parameters, such as factor loading, regression coeffiecant, latent variable variance and covariance, etc. The major purpose of the present article is to introduce the concepts and techniqures of power analysis and sample size planning in SEM study. Empirical examples followed by the step-by-step procedures were also provided. For the model fit testing, three types of fiting strategies: exact fit, close fit, and not close fit, were discussed in terms of power analysis and sample size determination. For the parameters of a model, the analysis of power depends upon the types and the amount of paremeters for estimating. The current article also provided several reference tables for determining the minimum sample size as well as the power of analysis, for both of model fit and paremeter estimation. In the end, the future development of power analysis and sample size determination was discussed.

並列關鍵字

Statistical power ； Sample size planning ； non-centrality parameter ； hypothesistesting