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