Deficiencies of combined rank tests

One-and two sample problems are considered which are divided into subproblems, for each of which a separate rank statistic is obtained. The best combination of these statistics is then compared to the ordinary undivided rank statistic. One easily sees that, under natural conditions, splitting causes no first order efficiency loss. Hence it becomes interesting to derive second order results. The required methods are rather technical but fortunately much can be built on earlier work. The results are simple and quite encouraging: enlarging the number of subgroups by one typically costs about one additional observation. A small simulation study confirms these results.