The Philosophy of Multiple Comparisons

This paper is based on the 1989 Miller Memorial Lecture at Stanford University. The topic was chosen because of Rupert Miller's long involvement and significant contributions to multiple comparison procedures and theory. Our emphasis will be on the major questions that have received relatively little attention--on what one wants multiple comparisons to do, on why one wants to do that, and on how one can communicate the results. Very little attention will be given to how the results can be calculated--after all, there are books about that (e.g., Miller, 1966, 1981; Hochberg and Tamhane, 1987).