假設一固定效應的變異數分析模型，其誤差項彼此獨立且誤差項服從常態分配但誤差變異數不相等且未知，在給定不同的水準和檢定力之下，對其因子效應是否相等的假設檢定進行研究。一個設計導向的兩階段抽樣程序法，是用來處理檢定之檢定力不受變異數影響的方法，同時決定在給定的水準和檢定力下所需的樣本數，以達成決策目的。兩階段抽樣程序法可導出不同檢定統計量的分配，同時這些分配和未知參數無關，據此，在虛無假設及對立假設下，可計算臨界值、檢定力及樣本數，所以可利用兩階段抽樣程序法進行因子效應是否相等的檢定。當兩階段抽樣程序法受限於成本預算、時間、實驗資料遺失或其它因素而無法執行完畢時，可採用分析導向的一階段抽樣程序法處理已有的資料。一階段抽樣程序法亦可導出不同檢定統計量的分配，所得到的分配和未知參數無關。因此，當二階段抽樣程序法無法完成時，一階段抽樣程序法可承接二階段抽樣程序法進行統計分析。本文針對二因子變異數分析含交互作用項模型和三因子變異數分析含交互作用項模型進行研究。

Assuming a fixed-effects ANOVA model where the error terms are independent and follow normal distributions with unequal and unknown variances in addition to unknown experimental factor effects, the interest is to test the hypotheses of various effects at a given level of significance and a given power. A design-oriented two-stage sampling procedure is employed to conduct various tests and simultaneously determine the necessary sample sizes at the fixed level and power. This is possible because the distributions of various test statistics under null hypothese are independent of all unknown parameters. Tables of critical values and design constants to meet the given level and the power are provided for practitioners. When the two-stage sampling procedure cannot be completed due to budget cut, time limit, missing experimental units or some other cost factors, a one-stage data analysis-oriented procedure can be employed to conduct the statistical tests based on available observations on hand. It can be seen that the distributions of the one-stage test statistics are also independent of all unknown parameters. As a result, the one-stage sampling procedure can supplement the two-stage sampling procedure to continue the statistical analysis to draw a conclusion. Two-way and three-way layout in ANOVA models with all interactions are studied and conclusions are made accordingly.

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