本研究的主要目的為：提議一個用以產生隨機效果p×i設計下，具有指定變異成分的二分資料的迭代程序，並且使用模擬方法檢查這個迭代程序是否真能產生具有指定變異成分的二分資料。另一個目的則是針對迭代程序產生的二分資料，使用折刀程序估計隨機效果p×i設計的變異成分估計量的標準誤以檢查折刀程序的估計表現。
研究結果顯示：就隨機效果p×i設計而言，迭代程序產生的二分資料的樣本平均變異成分都與其對應的指定變異成分非常接近；而對於二分資料，折刀程序在估計隨機效果p×i設計的變異成分估計量的標準誤的表現甚佳。

The main purposes of this study include to propose an iterative procedure for generating dichotomous data with pre-specified variance components in random effects p×i designs, and to examine whether this proposed iterative procedure can really generate dichotomous data desired. The additional purpose is to apply the Jackknife procedure to the generated dichotomous data to examine the performance of it in estimating standard errors of variance component estimators.
The simulation results showed that each average variance component of all random samples in the studied designs was very close to its corresponding pre-specified variance component for the generated dichotomous data, and the Jackknife procedure performed quite well in estimating standard errors of variance component estimators for the studied designs.

摘要 i
Abstract ii
目錄 iii
表格目錄 iv
圖片目錄 v
第一章 緒論 1
1.1 研究動機 1
1.2 使用變異數分析估計變異成分 3
1.3 相對誤差變異數與絕對誤差變異數 4
1.4 研究目的 7
第二章 相關文獻探討 9
2.1 估計變異成分估計量的標準誤：折刀法與靴環法 9
2.2 模擬具有指定變異成分的常態資料與多分資料 10
2.3 產生多分資料的方程式 11
第三章 研究方法 15
3.1 研究架構 15
3.2 模擬產生具有指定變異成分二分資料的迭代程序 15
3.3 說明迭代程序的可行性 19
第四章 研究結果 24
4.1 估計指定變異成分與誤差變異數的表現 24
4.2 折刀法估計變異成分估計量的標準誤的表現 28
第五章 結論 33
參考文獻 34

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