兩偏斜分配平均數比例之無母數信賴區間

Nonparametric Confidence Interval for the Ratio of Two Means from Skewed Distributions

蘇秀媛(Hsiu-Yuan Su) ； 林建佑(Chien-You Lin) ； 謝鑫能(Hsin-Neng Hsieh)

《Journal of Data Analysis》 5卷6期 (2010/12) Pp. 79-89

https://doi.org/10.6338/JDA.201012_5(6).0005

摘要

在醫藥研究中，測試新藥對於兩個不同試驗單位所產生之效應，以及在醫務管理研究中，診斷是否罹患重大疾病所需的支出等等，得到的資料往往呈現偏斜的分配。由於平均數能夠反映出整個群體中央趨勢的變化，研究者常對於兩獨立偏斜的母體平均數差或母體比例感到興趣。本研究主要是提出一個兩獨立偏斜分配平均數比例之無母數信賴區間（nonparametric confidence interval），並與拔靴法（bootstrap method）所建立之信賴區間來做比較。研究結果顯示在建立平均數比例之信賴區間時，無母數法較拔靴法有不錯的覆蓋機率（coverage probability），較拔靴法更接近95%的信賴水準，且其平均信賴區間長度亦較拔靴法所建立之區間為短。

關鍵字

拔靴法 ； 無母數法 ； 覆蓋機率

並列摘要

Health research often gives rise to data that are positive and highly skewed. In this study investigates the interval estimates for the ratio of two means by using proposed nonparametric method and bootstrap methods. Through a simulation study, the performance of nonparametric method provides not only sufficient coverage probability but also reasonable relative bias. The performance of nonparametric method is better than bootstrap method. Finally, the proposed method is illustrated with a real example.

並列關鍵字

Bootstrap ； nonparametric method ； coverage probability

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