中位数差值及置信区间的两种非参数计算方法及比较

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。

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

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.