臺灣博碩士論文加值系統

在列聯表的資料型態中，費雪精確檢定法被廣為運用在檢定個別母體比例是否相等的問題，在列聯表中邊際總數事先已知的情況下，此方法為一精確檢定法，但若應用於其他的資料型態上，例如臨床試驗中最常見的兩獨立二項分布母體，費雪精確檢定法將為一條件檢定法。多年來已有許多的數值驗證結果指出，以費雪精確檢定法檢定兩獨立二項分布母體比例是否相等的問題上，將會獲得比預期小的型I錯誤機率，以至於檢定結果將獲得較小的檢定力。而在現今亦有修正的檢定方法來提升其型I錯誤機率，例如：2008年Crans 和Shuster針對廢選精確檢定法提出一個修正方法，他們定義出新的顯著水準，α*=α+ε，α代表原先設定之顯著水準，ε代表一特定的正數。此方法藉由新的顯著水準來增加拒絕域內的樣本，進而提升型I錯誤機率以及其檢定力。其實早在1985年，Suissa和 Shuster 已提出以Student t-test統計量來建構其拒絕域的非條件下之精確檢定方法。至於這兩種方法現今並沒有任何結論於何者檢定方法較具有檢定力。因此，我們將給出一系列的數值結果說明這兩種方法的特性及優點。接著將二維有限樣本之確實檢定法以另一個觀點來歸納出其一般式，並將其推廣至分析高維度的離散資料。最後經由檢力函數之圖表來觀看各個推廣方法的曲線變化，進而瞭解各方法之優缺點。

Fisher's exact test (FET) is a conditional method that is frequently
used to analyze data in a 2×2 table for small samples. This
test is conservative and attempts have been made to modify the test
to make it less conservative. For example, Crans and Shuster (2008)
proposed adding more points in the rejection region to make the test
more powerful. Additionally, they propose an adjusted method that defines new significance levels α*=α+ε, where α is pre-specified and ε is a small positive number.
The adjustment uniformly improves the test size,
rasing the actual probability of type I error,
where the sequence of the possible outcomes for the rejection region is based on the p-value of FET.
Early in year 1985, Suissa and Shuster had proposed the exact unconditional method (EUM) used the t-test statistic with pooled and un-pooled variance, respectively, to derive a rejection region for the hypothesis.
In addition, up to now, there is no conclusion in which of these tests gives larger power,
we will give a series of numerical comparison to these two tests.
Later, we also extend these two test procedures to high dimensional problem.
Specifically, the extensions use several different combinations
to merge the information to form an univariate test statistic.
Lastly, some figures are presented to show the pattern changes of the power functions of these extensions.

1. Introduction
2. Test for two independent binomial samples
2.1. Exact unconditional method (EUM)
2.2. Modified Fisher's exact test(MFET)
3. Two dimensional rank function
4. Comparisons of the power of EUM, MFET and ECT in two independent binomial trial
5. High dimensional rank function
6. Comparisons of the power of the tests in three independent binomial trial
7. Discussion and conclusion
Appendix A. The C/C++ code of 2-dimensional ECT
Appendix B. The C/C++ code of 3-dimensional ECT

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