BALANCING TYPE-I AND TYPE-II ERROR PROBABILITIES - FURTHER COMMENTS ON PROOF OF SAFETY VS PROOF OF HAZARD

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 samples 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 "proof of safety", we recommend that consideration be given to equating Type I and Type II error probabilities at somewhat higher than the habitually-used levels in the "proof of hazard" test in order to reduce sample size requirements to attainable levels. To assist in the implementation of this approach, several charts that display the possible tradeoffs among the various decision quantities are given. The ideas and suggestions presented here apply as well in many areas of application aside from environmental health.