Multiple comparisons: philosophies and illustrations

Statistical procedures underpin the process of scientific discovery. As researchers, one way we use these procedures is to test the validity of a null hypothesis. Often, we test the validity of more than one null hypothesis. If we fail to use an appropriate procedure to account for this multiplicity, then we are more likely to reach a wrong scientific conclusion-we are more likely to make a mistake. In physiology, experiments that involve multiple comparisons are common: of the original articles published in 1997 by the American Physiological Society, approximately 40% cite a multiple comparison procedure. In this review, I demonstrate the statistical issue embedded in multiple comparisons, and I summarize the philosophies of handling this issue. I also illustrate the three procedures-Newman-Keuls, Bonferroni, least significant difference-cited most often in my literature review; each of these procedures is of limited practical value. Last, I demonstrate the false discovery rate procedure, a promising development in multiple comparisons. The false discovery rate procedure may be the best practical solution to the problems of multiple comparisons that exist within physiology and other scientific disciplines.