Determining sample sizes to guarantee variance reductions

 

Syntax

BD>findsize  :E

where E is any valid equation which results in a real positive number such that .

The FINDSIZE:  command is used to determine, by exploiting second-order exchangeability, the sample sizes required to guarantee requested levels of variance reduction in individual quantities and the system overall. Suppose that [B/D] currently holds the preliminary adjustment [B/C(n)] as detailed in §16.3. The output consists of the current and maximal resolutions for each and for overall, together with sample sizes and extra sample sizes to guarantee two alternative degrees of increase in resolution.

For the collection B considered as a whole, a row is output consisting of the following:

1. the name of the collection, B;
2. the current resolution in the collection, ;
3. the maximal resolution in the collection, ;
4. the smallest sample size such that ;
5. the smallest additional sample sise such that .

Then, for every element (output can be restricted to some subset of elements using the OPTION:  command), a row is output consisting of thhe following.

1. the name of the element, ;
2. the current resolution in the collection, ;
3. the maximal resolution in the collection, ;
4. the smallest sample size such that ;
5. the smallest extra sample size such that .

Hence, the penultimate column of output consists of sample sizes unconditionally guaranteed to achieve minimum resolutions in uncertainty for the collection and its individual elements. [B/D] indicates whenever the degree of resolution required is not achievable. The final column relates to effects in addition to the current adjustment, and shows the extra sample sizes required to guarantee extra degrees of resolution.

The kind of unconditional output seen in the penultimate column can be accessed for both the collection and its component elements by using the findsize  operator.