Non Response in Sampling From a Dichotomous Finite Population

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Non Response in Sampling From a Dichotomous Finite Population
Benjamin F King
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2. , The result, however, is long, and we shall not present it here, although it lends itself directly to computer programming for evaluation. ) The use of a well known trick enables us to avoid the need for Var'''(Ri+R2) in the determination of the optimal sample size.
7. OPTIMAL SAMPLING WITHOUT FOLLOW-UP If we intend to make a terminal estimate of R after the first sample of k respondents has been interrogated, then the optimal sample size is deter- mined by choosing n to minimize the prior
...expected value of the posterior expected loss; i. E. , /^ min E ' min E'''1(R, R, r, k, n) n '^ = min k^ E 'Var"(R)+k_+k-n, n (7. 1) %Iote that with the multivariate extension of a rectangular prior mass function, i. E. R{'=r2=s{=l, and n'=4, (6. 15) implies that one should consider half of the non-respondents to be favorable -- a kind of balance that is not surprising, since the posterior for R2 is highly dependent on prior assumptions.
20 by substitution from (6. 4).
In order to avoid direct formulation of Var(R) and subsequent application of the prior expectation operator^ we use the relation [ 5, p.


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