The Unreasonable Ineffectiveness of Fisherian Tests in Biology, and Especially in Medicine

Stephen T. Ziliak Roosevelt University Chicago, IL, USA [email protected] Abstract Biometrics has done damage with levels of R or p or Student’s t . The damage widened with Ronald A. Fisher’s victory in the 1920s and 1930s in devising mechanical methods of “testing,” against methods of common sense and scientific impact, “oomph.” The scale along which one would measure oomph is particularly clear in biomedical sciences: life or death. Cardiovascular epidemiology, to take one example, combines with gusto the “fallacy of the transposed conditional” and what we call the “sizeless stare” of statistical significance. Some medical editors have battled against the 5% philosophy, as did, for example, Kenneth Rothman, the founder of Epidemiology. And decades ago a sensible few in education, ecology, and sociology initiated a “significance test controversy.” But, grantors, journal referees, and tenure committees in the statistical sciences had faith that probability spaces can substitute for scientific judgment. A finding of p < .05 is deemed to be “better” for variable X than p < .11 for variable Y . It is not. It depends on the oomph of X and Y—the effect size, size judged in the light of how much it matters for scientific or clinical purposes. In 1995 a Cancer Trialists’ Collaborative Group, for example, came to a rare consensus on effect size: 10 different studies had agreed that a certain drug for treating prostate cancer can increase patient survival by 12%. An 11th study published in the New England Journal in 1998 dismissed the drug. The dismissal was based on a t-test, not on what William Gosset (the “Student” of Student’s t) had called, against Ronald A. Fisher’s machinery, “real” error.1