Anticarcinogenicity in a long-term rodent bioassay is defined as a statistically significant decrease of a specific tumor type in a dosed group following chemical exposure. About 92% of chemicals tested by the National Toxicology Program prior to 1983 reveal at least one site with a significant (p < or = 0.05) tumor rate decrease in one or more tested groups, a result consistent with those of J. K. Haseman and F. M. Johnson (1996, Mutat. Res. 350, 131-141) for a database of recently tested chemicals. Detection of tumor decreases in a specific site can be explained not only by biological effects, but also as a result of random variability in the background tumor rates, decreases in body weight, or decreases in survival of treated animals. This paper evaluates the rate of false-positive anticarcinogenic findings due to random effects (variations in tumor rates and the multiple comparisons undertaken in evaluating a bioassay), while a companion paper addresses the influence of weight and survival depression. Monte-Carlo simulation was conducted to assess the contribution of random effects. This contribution was found to be important even when a statistical significance cutoff of p0 < or = 0.05 was chosen. If a more stringent statistical criterion was used (p0 < or = 0.01 or p < or = 0.005), the proportion of false positive determinations diminishes. The number of anticarcinogens in the database remains substantially higher than predicted by the stimulations. An examination of the distribution of all p values (T. Schweder and E. Spjøtvoll, 1982, Biometrika 69, 493-502) also indicates that statistically significant anticarcinogenic responses are found in the database at a higher rate than would result from purely random responses. Finally, the cross-species prediction of anticarcinogenic responses was examined in a manner similar to a study of cross-species prediction of carcinogenic responses (G. M. Gray et al., 1995, Reg. Toxicol. Pharmacol. 20, 281-301). The analyses show that anticarcinogenic effects in one rodent species predict well anticarcinogenic effect in another rodent species. It seems likely that biological factors are involved in anticarcinogenic responses observed in rodent cancer bioassays.