(Received January 17, 1994; revised July 5, 1994)
Abstract. Although the theory of rank tests is rather complete in the one-sided case, it was not even known in 1959, whether the Wilcoxon two-sample test and other similiar tests are unbiased against the two-sided alternatives (Lehmann (1959, Testing Statistical Hypotheses, p. 240, Wiley, New York)). A partial answer to this question was given by Sugiura in 1965, who found, that the test named above may be biased (Sugiura (1965, Ann. Inst. Statist. Math., 17, 261-263)). According to Lehmann (1986, Testing Statistical Hypotheses, 2nd ed., pp. 322-324, Wiley, New York) it seems to be still open, whether the same is true for the WILCOXON one-sample test, which is also known as WILCOXON signed rank test. This will be shown in the present paper.
Key words and phrases: Rank test, unbiasedness, counter-example.