A step-down multiple hypotheses testing procedure that controls the false discovery rate under independence

For the problems of multiple hypotheses testing, Benjamini and Hochberg (1995, J. Roy. Statist. Sec. Ser. B 57, 289-300), proposed the control of the expected ratio of the number of erroneous rejections to the number of total rejections, the false discovery rate (FDR). The step-up procedure given in that paper controls the FDR when the test statistics are independent. In this paper, a new step-down procedure is presented, and it also controls the FDR when the test statistics are independent. The step-down procedure neither dominates nor is dominated by the step-up procedure. In a large simulation study of the power of the two procedures, the step-down procedure turns out to be more powerful when the number of tested hypotheses is small and many of the hypotheses are far from being true. An example is given to illustrate the step-down procedure. (C) 1999 Elsevier Science B.V. All rights reserved. MSG: 62J15.