Sample Design and Sample Size for Single-Stage Surveys

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Chapter 3 covers the problem of determining a sample size for single-stage surveys with imposed constraints such as a desired level of precision. To determine a sample size, a particular type of statistic must be considered. Means, totals, and proportions are emphasized in this chapter. We concentrate on simple random samples selected without replacement in Sect.3.1. Precision targets can be set in terms of coefficients of variation or margins of error for unstratified designs as discussed in Sect. 3.1.1. We cover stratified simple random sampling in Sect. 3.1.2. Determining a sample size when sampling with varying probabilities is somewhat more complicated because the without-replacement variance formula is complex. A useful device for determining a sample size when sampling with probability proportional to size (pps) is to employ the design-based variance formula for with-replacement sampling, as covered in Sect. 3.2.1. Although we mainly cover calculations based on design-based variances, models are also especially useful when analyzing pps sampling as discussed in Sect. 3.2.2.