The confidence of an optimal sampling size based on previous data - ARCHIVED

This paper discusses in detail issues dealing with the technical aspects of designing and conducting surveys. It is intended for an audience of survey methodologists.

For a multivariate survey based on simple random sampling, the problem of calculating an optimal sampling size becomes one of solving a stochastic programming problem in which each constraint corresponds to a bounded estimate of the variance for a commodity. The problem is stochastic because the set of data collected from a previous survey makes the components of each constraint random variables; consequently, the calculated size of a sample is itself a random variable and is dependent on the quality of that set of data. By means of a Monte Carlo technique, an empirical probability distribution of the optimal sampling size can be produced for finding the probability of the event that the prescribed precision will be achieved. Corresponding to each set of previously collected data, there is an optimal size and allocation across strata. While reviewing these over several consecutive periods of time, it may be possible to identify troublesome strata and to see a trend in the stability of the data. The review may reveal an oscillatory pattern in the sizes of the samples that might have evolved over time due to the dependency of one allocation on another.