The implementation of a number of chemical carcinogen screening programs was accompanied by the observation that some screens might have high false positive error rates. With designs presently used at the National Cancer Institute and historical spontaneous tumor rates based on control animals in previous experiments, upper bounds were computed on the false positive error rates for several screening strategies. False positive results are less likely to occur at tissue sites with low spontaneous tumor rates. The site at which a significant tumor increase occurs is important. There is danger in relying solely on the finding of statistical significance without incorporating biological knowledge and corroborative evidence such as the presence of a dose-response relationship or experimentally consistent results in different species or sexes. A report by the National Cancer Institute Carcinogenesis Program demonstrates these concepts.