Optimal Allocation of Observations when Comparing Several Treatments with a Control. Ii. 2-Sided Comparisons

摘要

Let P sub O, P sub 1, ..., P sub p be p+1 normal populations with unknown population means (u sub p) and known population variances. P sub O is referred to as the 'control' population and P sub i (1 less than or equal to i less than or equal to p) as the (i)th 'test' population. Based on N sub i independent observations X sub ij (j=1,2,..., N sub i) from P sub i (i=0,1,...,p) where N = the sum over i from 0 to P of N sub i and constants r greater than or equal to 0, d>0 are specified prior to experimentation, it is desired to make an exact confidence statement of the form (1) (mean(x sub O)-mean(x sub i)-d