Gradually Confidence Interval On The Toxicity Evaluation Of Packet Data

With the development of drugs production techniques, people are paying more attention to the toxicity of drugs. Toxicological study is playing an important role in the modern drug development. To a new drug, proper-statistics methods of toxicological evaluation are of importance. In toxicological studies,it is desirable for a method to not declare a higher dose to be safe if it does not declare a lower dose to be safe,Hsu and Berger(1999)'s stepwise confidence interval method was recently proposed for this purpose. Hsu and Berger(1999)W have proposed an useful stepwise confidence interval method for toxicity studies, assuming the variance is equal under normal population. Recently, tao, guo and shi(2002)have proposed a stepwise confidence interval procedure without the homoscedasticity by the application of the Stein's two-stage sampling method, so providing a more extensive field to solve practical problems.In the stepwise confidence interval procedure proposed by Hsu and Berger(1999)and Tao, guo and shi(2002), only after obtaining the exact values of the observations under normal population, can they use the stepwise confidence interval procedure. But in fact, sometimes we can run across this problems: we can not obtain exact values of the observations but know the numbers of observations falling in each groups, the numbers are usually said to be grouped samples. In this paper, we assume observations are made from normal population, yet we do not know the exact observations, and only know the numbers of observations falling in each groups, these numbers are called grouped samples. Recently, shi et al(2001) and gao et al(1999) provide a useful results for grouped samples. In our paper, some important results are made from their papers. In this article, we extend their stepwise confidence interval procedure for grouped samples, proposing a stepwise confidence interval method for grouped samples. In addition, we have given a proof that the family-wise type I rate can be controlled at the pre-chosen nominal level.