在現實的抽樣調查中，集群抽樣、分層抽樣與二階段抽樣皆是常見的抽樣方法，不同的抽樣方法各有其利與弊，為了在集群抽樣的情況下能夠對母體中各層的參數做估計，在兼顧抽樣便利性以及分層實用價值的同時，第二階段的樣本選擇也能更有彈性，因此本篇論文提出了整合第二階段樣本之修正二階段抽樣（Modified two-stage sampling designs with integrated second-stage sample）。
修正二階段抽樣的抽樣流程分為兩個階段，第一階段先從母體抽出主要單元樣本，接著在第二階段時將每個主要單元樣本包含的次要單元整合視為次母體，再從次母體中抽出次要單元樣本。修正二階段抽樣的第一階段和第二階段可以選擇任意的抽樣方法，因其搭配不同的抽樣方法而有不同的形態，在本篇論文中提出三種由傳統抽樣方法組合而成的修正二階段抽樣，並且說明不同修正二段抽樣的實際應用和參數估計過程，在推導母體總和估計量以及其變異數、變異數估計的過程中也分別證明了估計量的不偏性，從模擬的結果觀察不同情況下估計量的表現。此外，在本篇論文中亦將修正二階段抽樣和傳統二階段抽樣一同此較以檢視其表現，並發現修正二階段抽樣的母體總和估計量在精準度上有一定程成之精進。

In real-world sampling surveys, cluster sampling, stratified sampling, and two-stage sampling are common sampling methods. Each sampling method has its own advantages and disadvantages. In order to estimate parameters of each stratum in the population under cluster sampling, while considering both sampling convenience and the practical value of stratification, the selection of samples in the second stage can be more flexible. Therefore, this paper proposes a Modified Two-stage Sampling Design with Integrated Second-stage Sample.
The sampling process of the modified two-stage sampling consists of two stages. In the first stage, primary unit samples are drawn from the population, and then in the second stage, each primary unit sample is regarded as a subpopulation, from which secondary unit samples are drawn. The first and second stages of the modified two-stage sampling can use any sampling method, resulting in different forms depending on the combination of sampling methods. In this paper, three modified two-stage sampling designs composed of traditional sampling methods are proposed, and their practical applications and parameter estimation processes are explained. The unbiasedness of the estimated population total and its variance, as well as variance estimation, are demonstrated during the derivation process. The performance of the estimates under different scenarios is observed from the simulation results. Additionally, the performance of the modified two-stage sampling is compared with traditional two-stage sampling, revealing an improvement in the precision of the estimated population total under the modified two-stage sampling.

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