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| Title: | 簡單順序假設波松母數較強檢力檢定研究- 兩兩母均數比例
More powerful tests for simple order Hypotheses about Poisson parameters --- the ratios of the parameters |
| Authors: | 潘彥丞
Pan, Yen Chen |
| Contributors: | 劉惠美
Liu, Hui Mei
潘彥丞
Pan, Yen Chen |
| Keywords: | 波松分布
信賴區間p-value
較強檢定力檢定
Poisson distribution
Confidence interval p-value
More powerful test |
| Date: | 2017 |
| Issue Date: | 2017-07-11 11:26:30 (UTC+8) |
| Abstract: | Roger L. Berger (1996) “More Powerful Tests from Confidence Interval p Values”在檢定兩獨立二項分布時，先建立非條件檢定z-test，找到非條件檢定之p-value，以p_z表示，接著引用Roger L. Berger and Dennis D. Boos (1994) “P Values Maximized Over a Confidence Set for the Nuisance Parameter”將最大化取值的界限限制在信賴區間內，找到的信賴區間之p-value (Confidence interval p-value)，以p_c表示，欲針對非條件檢定建構較強檢定力之檢定，亦即檢定尺度依然小於α 並且檢定力較強之檢定，結果發現以p_z≤α找到之拒絕域包含於用p_c≤α找到之拒絕域，等同於用p_c找到之拒絕域其檢定力至少較p_z為高，亦即Berger (1996)引用Berger and Boos (1994)的方法，成功建構較非條件檢定還要強之檢定。
而本文將引用Berger (1996)的方法將兩獨立波松分布進行套用，希望檢定兩波松分布之母均數比例，應用Hon Keung Tony Ng and Man-Lai Tang (2005) ” Testing the equality of two Poisson means using the rate ratio”建立出非條件檢定z-test，並且根據Berger and Boos (1994)的方法，利用Robert M. Price and Douglas G. Bonett (2000) “Estimating the ratio of two Poisson rates”找到之信賴區間，建立信賴區間之p-value，得出較非條件檢定還要強之檢定。
我們發現在進行實驗設計時，兩獨立波松分布之樣本數比例是很重要的變數，它會影響我們找到之較強檢定力之檢定的表現，在廣泛的領域應用上，將此變數控制為理想的值勢必可以達到提升實驗效率並且降低研究之成本。
In the problem of comparing two independent binomial populations , Roger L. Berger (1996) “More Powerful Tests from Confidence Interval p Values.” showed that the test based on the confidence interval p-value of Roger L. Berger and Dennis D. Boos (1994) “P Values Maximized Over a Confidence Set for the Nuisance Parameter.” often is uniformly more powerful than the standard unconditional test.
In this article we consider the problem of comparing two independent poisson population rates ratio. Based on the Hon Keung Tony Ng and Man-Lai Tang (2005) ” Testing the equality of two Poisson means using the rate ratio” , we construct the standard unconditional z-test . Similarly, based on the Berger and Boos (1994),we use the confidence interval from Robert M. Price and Douglas G. Bonett (2000) “Estimating the ratio of two Poisson rates” to construct the confidence p-value. We show the confidence p-value is more powerful than the standard unconditional z-test.
The sample ratio of two independent poisson is an important variable, it controls the influence of the more powerful test. In a wide range of applications , the control of this variable to the ideal value is bound to achieve improved experimental efficiency and reduce the cost of the experiment. |
| Reference: | 1. Clopper, C. J., and Pearson, E. S. (1934). “The use of Confidence or Fiducial Limits Illustrated in the Case of the Binomial”. Biometrika, 26, 404-413.
2. Haber,M. (1986). “An Exact Unconditional Test for the 2×2 Comparative Trial”. Psychological Bullein, 99, 129-132
3. Hon Keung Tony Ng and Man-Lai Tang (2005). ” Testing the equality of two Poisson means using the rate ratio”. Statistics in Medicine, 24, 955-965.
4. K.Krishnamoorthy and Jessica Thomson (2002). “A more powerful test for comparing two Poisson means”. Journal of Statistical Planning and Inference, 119, 23-35.
5. Lehmann, EL (1952), “Testing multiparameter hypotheses”. The Annals of Mathematical Statistics, 541-552.
6. Roger L. Berger and Dennis D. Boos (1994). “P Values Maximized Over a Confidence Set for the Nuisance Parameter”. Journal of the American Statistical Association, 89, 1012-1016.
7. Roger L. Berger (1996). “More Powerful Tests from Confidence Interval p Values”. The American Statistician, 50, 314-318
8. Robert M. Price and Douglas G. Bonett (2000). “Estimating the ratio of two Poisson rates”. Computational Statistics & Data Analysis, 34,345-356.
9. Suissa, S., and Shuster,J. J. (1985). “Exact Unconditional Sample Sizes for the 2×2 Binomial Trial”. Journal of the Royal Statistical Society,Ser. A,148,317-327.
10. Thode HC. (1997). “Power and sample size requirements for tests of differences between two Poisson rates”. The Statisticain, 46, 227-230.
11. Data.gov，美國交通違規事件，上網日期2017年6月15日，檢自：https://catalog.data.gov/dataset/traffic-violations-56dda |
| Description: | 碩士
國立政治大學
統計學系
104354016 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G1043540161 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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