COMPARISON OF SOME STATISTICAL EXPERIMENTS ASSOCIATEDWITH SAMPLING PLANS
Erik Torgersen
Abstract: Some experiments occurring in sampling theory may be described as
follows:
Consider a finite population and a characteristic of interest which, with varying
amount (value, degree, etc.), is possessed by all individuals in . Let be the amount of
this characteristic for an individual .
It is known that belongs to some set of functions on .
Let be a sampling plan, i.e. a probability distribution on the set of finite sequences of
elements from . If this sampling plan is used and if the characteristics of sampled
individuals are determined without error, then the outcome
is
obtained with probability
Let denote the experiment obtained by observing and assume that is not too
small. Then is at least as informative as if and only if the sampled subset under
is ”stochastically contained” in the sampled subset under Using the theory of
comparison of statistical experiments we shall here discuss this and other related
results.
and a characteristic of interest which, with varying
amount (value, degree, etc.), is possessed by all individuals in 
. Let 
be the amount of
this characteristic for an individual 
.
belongs to some set 
of functions on 
.
be a sampling plan, i.e. a probability distribution on the set of finite sequences of
elements from 
. If this sampling plan is used and if the characteristics of sampled
individuals are determined without error, then the outcome
denote the experiment obtained by observing 
and assume that 
is not too
small. Then 
is at least as informative as 
if and only if the sampled subset under
is ”stochastically contained” in the sampled subset under 
Using the theory of
comparison of statistical experiments we shall here discuss this and other related
results.