中位数差值及置信区间的两种非参数计算方法及比较

中国临床药理学与治疗学 ›› 2012, Vol. 17 ›› Issue (7): 761-767.

中位数差值及置信区间的两种非参数计算方法及比较

李云飞¹, 王鲲^1,2, 黄继汉¹, 盛玉成¹, 何迎春¹, 郑青山^1,2

¹上海中医药大学药物临床研究中心,上海 201203;
²上海高校中医内科学E-研究院(上海中医药大学),上海 201203

收稿日期:2011-10-10 修回日期:2012-03-07 发布日期:2012-07-17
通讯作者: 王鲲,男,博士,副研究员,研究方向:定量药理学。Tel: 021-51322420 E-mail: kunwang@139.com
郑青山,男,教授,博士生导师,研究方向:定量药理学、生物统计学。Tel: 021-51323006 E-mail: zhengqscn@21cn.com
作者简介:李云飞,男,在读博士,研究方向:定量药理学和生物统计学。Tel: 021-51322420 E-mail: liyunfei718@sina.com
基金资助:
上海市教委基金资助项目 (09JW17);上海市教委创新项目(10YZ61);上海市教委E研究院建设计划项目(E03008);高等学校博士学科点专项科研基金项目 (20103107120014)

Two non-parametric methods and its comparation for calculating median difference and its confidence interval

LI Yun-fei¹, WANG Kun^1,2, HUANG Ji-han¹, SHENG Yu-cheng¹, HE Ying-chun¹, ZHENG Qing-shan^1,2

¹Center for Drug Clinical Research,Shanghai University of Traditional Chinese Medicine, Shanghai 201203, China;
²E-institute of Internal Medicine of Traditional Chinese,Shanghai University of Traditional Chinese Medicine, Shanghai 201203, China

Received:2011-10-10 Revised:2012-03-07 Published:2012-07-17

摘要/Abstract

摘要： 目的: 介绍了两种计算中位数差值及置信区间的非参数方法——Hodges-Lehmann法与Bootstrap法,采用三种不同分布数据实例比较分析两种方法间的差异,对差异产生原因进行了分析。 方法: 用计算机模拟的方法生成正态、对数正态和双峰分布数据各两个,用两种非参数方法计算每种分布的中位数差值及其置信区间。该模拟过程重复500次。 结果: 当数据符合正态分布时两种方法的结果相近,且与用均值取代中位数的参数法接近。当数据为对数正态分布时Bootstrap法的估计值及置信区间比Hodges-Lehmann法偏大,当数据为对称分布时两种方法计算的估计值结果相近,置信区间略有差异。 结论: 对称分布的数据两种方法的估计值基本一致。非对称情况下Bootstrap法更注重中位数的位置,而Hodges-Lehmann法更多体现了数据的值的差异。

关键词: 非参数检验, 中位数差值置信区间, Bootstrap, Hodges-Lehmann

Abstract: AIM: To introduce two nonparametric methods (Bootstrap and Hodges-Lehmann) for calculating median difference and its confidence interval; the results of these two methods were compared under three pairs of data from three different distributions, and the reason of the difference was discussed. METHODS: Two groups of data were generated from each normal, lognormal and bimodal distribution by computer simulation. The median difference and its confidence interval of each pair were calculated by the two nonparametric methods. This process was repeated for 500 times. RESULTS: The results of the two methods were nearly when data follow normal distribution and it's also agree with the results of parametric method by using mean instead median. For lognormal distribution, the estimated value of median difference and its confidences interval calculated by Bootstrap was larger than the results of Hodges-Lehmann. The results of the two methods was nearly when data distribution was symmetric while the confidence interval was slightly different. CONCLUSION: The two methods are coincident in symmetric distribution. However, Bootstrap emphasizes the position of median while Hodges-Lehmann cares the variance in the case of asymmetric distribution.

Key words: Nonparametric tests, Confidence interval of median difference, Bootstrap, Hodges-Lehmann

中图分类号:

R311

李云飞, 王鲲, 黄继汉, 盛玉成, 何迎春, 郑青山. 中位数差值及置信区间的两种非参数计算方法及比较[J]. 中国临床药理学与治疗学, 2012, 17(7): 761-767.

LI Yun-fei, WANG Kun, HUANG Ji-han, SHENG Yu-cheng, HE Ying-chun, ZHENG Qing-shan. Two non-parametric methods and its comparation for calculating median difference and its confidence interval[J]. Chinese Journal of Clinical Pharmacology and Therapeutics, 2012, 17(7): 761-767.

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