集群抽樣與分層抽樣皆為在現實的抽樣調查中常見的抽樣方法，兩種方法各有其利與弊，前者的優點為對母體及次母體的推估維持良好的精確度，而後者則是以抽樣便利性做為考量的抽樣方法。在執行一大規模的抽樣調查，撙節抽樣成本常為現實的首要考量，因而採用二階段或多階段的分層抽樣方法，其方法的缺點為犧牲部分的推估精確度，且無法控制次母體的樣本數量進而對其參數做推估。
為兼顧推估精確度及分層實用價值，並希望第二階段的樣本選擇能更有彈性，本篇論文提出了一修正的二階段抽樣設計。首先用任意的抽樣方法選取第一階段樣本，整合其所包含的所有第二階段樣本單元做為第二階段的抽樣母體，再進行第二階段抽樣，其中亦考量兩階段分別採用的抽樣方法，根據不同的抽樣方法組合提出相對應的估計量。此方法不僅保留了二階段抽樣設計之抽樣便利性，在其兩階段利用適當的抽樣設計組合使得推估精確度有一定程度之精進，同時與一般常見的抽樣設計（簡單隨機抽樣、集群抽樣與傳統二階段抽樣）一同比較以檢視其表現。此外，本篇論文亦使用2015 年的農林魚牧普查資料進行實例分析，以檢視此修正的二階段抽樣設計應用在實際資料之表現。

As two of the most commonly used sampling designs in practice, nevertheless cluster sampling and stratified sampling have somewhat contradict purposes. Estimation precision is usually better in stratified sampling, and proper stratification also can be apt for the estimation of a subpopulation of interest. On the other hand, sampling cost can be reduced in cluster sampling at the expense of losing precision in estimation result. In a large scale sampling survey situation, a two- or multi-stage cluster sampling is often investigator’s necessary choice to save the sampling effort. Consequently, estimation precision would be sacrificed, and often it would be difficult to estimate the subpopulation of interest since secondary sampling units are independently selected within each selected primary sampling units, hence, the within-subpopulation sample size often cannot be controlled.
A modified two-stage cluster sampling design will be constructed and investigated in this research. A set of primary units is selected in the first stage by some probability design, and then the sampling population of the second-stage sampling is composed of the integration of all the secondary units within the selected primary units. Therefore, the second-stage sample can be selected with more flexibility. For example, a stratified sampling design can be used so that the within-subpopulation sample size can be controlled, it can also be helpful to compensate the loss of estimation precision due to the cluster design used. The sampling cost is also reduced since the potential sampled units are restricted within the selected first-stage sample. Various combinations of the first- and second-stage designs are studied together with different estimators to investigate the property of this sampling design. The performance are compared with other comparable conventional designs including simple random sampling, classical two-stage sampling and stratified sampling. In addition to a pseudo population, the primary agricultural household population based on the 2015 Agriculture, Forestry, Fishing and Animal Husbandry Census is used to illustrate the practical advantage of this two-stage sampling scheme with integrated second-stage sample.

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