在許多實際情形下，傳統的統計檢定方法是不足以應付的。故本論文提出模糊檢定方法，我們定義出模糊樣本期望值與模糊樣本變異數的計算方法，再針對不同的模糊資料，分別提出不同的檢定方法，去解決最實際需要解決的問題，其中包括推廣古典的統計檢定方法與自創的檢定方法。 關鍵字：隸屬度函數，模糊樣本取樣，模糊樣本期望值，模糊樣本變異數，人性思考，t檢定，F檢定，模糊常態分配。 / In many expositions of fuzzy methods, fuzzy techniques are described as an alternative to a more traditional statistical approach. In this paper, we present a class of fuzzy statistical decision process in which testing hypothesis can be naturally reformulated in terms of interval-valued statistics. We provide the definitions of fuzzy mean, fuzzy distance as well as investigation of their related properties. We also give some empirical examples to illustrate the techniques and to analyze fuzzy data. Empirical studies show that fuzzy hypothesis testing with soft computing for interval data are more realistic and reasonable in the social science research. Finally certain comments are suggested for the further studies. We hope that this reformation will make the corresponding fuzzy techniques more acceptable to researchers whose only experience is in using traditional statistical methods. Key words: Membership function, fuzzy sampling survey, fuzzy mean, human thought, t-test, F-test, normally distributed.

分析具有巢狀誤差結構的迴歸模式時，惹忽略隨機誤差項之間的相關性，而採用最小平方(OLS)估計量所導出的標準 F 統計量（以 F^S表之）進行檢定，會導致過大的型 I 錯誤機率；若將隨機誤差項之間的相關性納入考量，而採用廣義最小平方(GLS)估計量所導出的 F 統計量 （以 F^GLS表之），則計算上會較為繁雜。因此我們藉由轉換方式，將模式轉換成隨機誤差項之間彼此獨立的新模式後，再以 F^S 進行檢定，其結果與直接以 F^GLS 檢定相同，且可使計算較為方便。由於模式轉換所需的轉換矩陣為母體變異數的函數，因此當母體變異數未知時，我們以 Henderson 的常數配適 （fitting-of-constants）方法來估計之。藉由模擬結果得知，若各段的觀察個數相等，則不論巢狀誤差結構為二段式(two-stage)或三段式(three-stage)，廣義最小平方估計量(GLS)均較最小平方估計量(OLS)表現穩定，且 F^GLS 在檢定力及實際顯著水準方面的表現也都比 F^S 好。 / When analyzing the regression model with nested-error structure, if the correlations between errors are ignored, and conduting the model adequacy test by the standard F statistic (F^S) led from the ordinary leastsquares estimator (OLSE) , then the type I error rate will be inflated. However, if the corrlated structure is considered and the model is tested by F^GLS led from the general least-squares estimator (GLSE) , the calculation will be more complicate. The model can be transformed to a new model with independent random errors and then, tested by F^S . The result is the same as the one by F^GLS , also it is more convenient for calculation. Since the transformation matrix is a function of variance components, we estimate variance components by Henderson's fitting-of-constants when they are unknown. Through simulation, it is concluded that if the observations in each stage of nested-error structure are the same, the GLSE is more stable than the OLSE in both two-stage and tree-stage structures. Also, the power and the sizes of F^GLS will perform better than those of F^S .