12-double sampling - ` ` We would like to use...

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1 ` We would like to use stratification, or ratio estimation to increase the precision of our estimator but the sampling frame has no information on the useful auxiliary variables. ` For example, we want to estimate the total timber volume by taking sample of truckloads of logs. Timber volume is related to the weight of the truckload. We could gain precision through ratio estimation. But weighing every truck in the population is impractical. Two-phase Sampling Suppose the population has N sampling units. The sample is taking in two phases: 1. Phase I sample. Take a probability sample of n (1) unit, called the phase I sample. Measure the auxiliary variables for every unit in the phase I sample. 2. Phase II sample. Act as though the phase I sample is a population and select a probability sample from the phase I sample. Measure the variables of interest for each unit in the subsample. Remark: Two-phase sampling can save time and money if the auxiliary information is relatively inexpensive to obtain and if having that auxiliary information can increase the precision of the estimate for quantities of interest.
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