In 1980, the Occupational Safety and Health Administration asserted that “non-positive human studies” would be considered in reviews of evidence only if in a study the “group of exposed subjects was large enough for an increase in cancer incidence of 50% above that in unexposed controls to have been detected at any of the predicted sites.” The concepts of statistical testing and power in occupational mortality studies are reviewed, and studies published in two prominent occupational health journals in 1979 and 1980 are analyzed in terms of their power. A large proportion of standardized mortality ratio studies have a low probability of detection of relative risks of the order of 1.5.