Theory of Sample Surveys by M. E. Thompson (auth.)

By M. E. Thompson (auth.)

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For example, the households of a city might be grouped into city blocks of households. At the first stage of sampling, a sample of PSUs is taken; and subsequently elementary units are sampled from within the selected PSUs according to some scheme, which may itself be conducted in stages. In rural areas of Canada the Canadian Labour Force Survey at one time used four stages in its sampling of households. Sampling in stages generally results in samples which are geographically clustered to some extent.

L). 84), but it yields a derivation of variance estimates more easily. First of all, Varl (els" r = 1, ... , L) is a function of tl, ... , tL. 23) Varl (els" r L = 1, ... " where V2,r is the variance of tr with respect to stages of sampling after the first. 90) where V2,r is an unbiased estimate of V2,r from the y values in s" d;(SB) satisfies the same unbiasedness condition as dr (s B), and VI is an unbiased estimate with respect to the first-stage design of Varl (elsr , r = 1, ... , L). This principle for forming variance estimates was given by Rao (1975), having been put forward in a less general context by Durbin (1953).

The problem is to determine the overall sample size n, and the allocation fractions nh/n, h = 1, ... , H, so as to minimize Var{Yst) subject to the total cost not exceeding C. 48) subject to the constraint H C= Lnhch. 50) allows solution for the overall sample size n. Note that we are optimizing over real values of {nh} and n; in actual surveys it is necessary to take the nh and n values to be integers near their optimal values. 8 depends on the y array at hand, through the relative values of the stratum variances S~.

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