Kafadar proposed a method of comparing biweight measures of location corresponding to two independent groups. Motivated by results under the assumption that distributions are symmetric, her method approximates the null distribution of the test statistic with a Student's t distribution having degrees of freedomare the number of observations randomly sampled from the respective groups. A minor goal in this paper is to illustrate that this approximation can be unsatisfactory when distributions have different levels of skewness. Four alternative procedures are considered, each based on the bootstrap. Three of these procedures provide satisfactory probability coverage when sample sizes are equal, while one provides good probability coverage in all situations that were considered.