Abstract
The frequently used way of comparing two independent groups is to compare in terms of some measure of location such as mean. For non-normal and heteroscedastic cases, trimmed mean, median or some other robust measures of location can be used instead. However, determination of the differences in the tails of the groups might be of interest. For this reason, comparing the lower and upper quantiles becomes an important issue. In this study, Harrell-Davis estimator and the default quantile estimator of R are compared in terms of actual Type I error rates. When quantiles close to zero or one are compared with small sample sizes Gumbel's estimator, and when quantiles close to median are compared with large sample sizes Harrell Davis estimator saved actual Type I error rate better.
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