Robustness of S1 with Hodges-Lehmann

The classical methods for comparing groups can be highly inefficient under the influence of non-normal and heteroscedastic settings.Investigators are looking for alternatives which are more flexible in terms of assumptions.Robust methods are known to be one such alternative.This study looks into S 1 statistic, flexible method for comparing groups using median as the location estimator.Works on S 1 mostly focussed on the searching of a more favorable alternative of the standard error of sample medians to achieve better control of Type I error.In this study, instead of targetting on the standard error, the investigation on the S1 statistic focusses on the sample median itself.The modified S1 statistic replaced the medians with Hodges-Lehmann and the default scale estimator with the variance of Hodges-Lehmann and MAD n to produce two different test statistics for comparing groups.Since the sampling distributions of these modified S1 statistics are unknown, bootstrap method was used for testing the hypotheses.The performance of the proposed statistic was measured in terms of Type I error and compared against the original S1 statistic.The propose procedures, generated conservative Type I error rates and on par with the original S 1 statistic for most of the conditions