This paper elaborates on earlier contributions of Bross (1985) and Millard (1987) who point out that when conducting conventional hypothesis tests in order to “prove” environmental hazard or environmental safety, unrealistically large sample sizes are required to achieve acceptable power with customarily-used values of Type I error probability. These authors also note that “proof of safety” typically requires much larger sample sizes than “proof of hazard”. When the sample has yet to be selected and it is feared that the sample size will be insufficient to conduct a reasonable.