The variance of the usual estimator in a stratified sampling design is given by V^2=sumh=1^LWh^2Sh^2/nh(1-fh) in the standard notations. We wish to obtain an allocation that minimizes the sample size. Then,

(D) the optimal allocation is the one for which nh is proportional to WhSh

Q167Section III (Statistics)167 of 190

Neyman allocation minimizes sample size for a fixed target variance

The variance of the usual estimator in a stratified sampling design is given by $V^2=\sum_{h=1}^L\dfrac{W_h^2S_h^2}{n_h}(1-f_h)$ in the standard notations. We wish to obtain an allocation that minimizes the sample size. Then,

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