ABSTRACT
Many statistical procedures applicable to the two-sample problem are based on the rank order statistics for the combined samples since various functions of these rank order statistics can provide information about the possible differences between populations. Many commonly used two-sample rank tests can be classified as linear combinations of certain indicator variables for the combined ordered samples. Such functions are often called linear rank statistics. Although all of the two-sample rank tests are for the same null hypothesis, particular test statistics may be especially sensitive to a particular form of alternative, thus increasing their power against that type of alternative. The very generality of linear rank tests makes it difficult to make direct comparisons of power functions since the calculation of power requires more specification of the alternative probability distributions and moments. For example, a particular test might have high power against normal alternatives but perform poorly for the gamma distribution.
