 For the Cauchy distribution (Student t-distribution with one degree of freedom), the Hodges-Lehmann is infinitely more efficient than the sample mean, which is not a consistent estimator of the median.For non-symmetric populations, the Hodges-Lehmann statistic estimates the population's "pseudo-median", a location parameter that is closely related to the median.The difference between the median and pseudo-median is relatively small, and so this distinction is neglected in elementary discussions.