Stratified sampling examples

Revision as of 19:19, 16 December 2010

Example 1

This example shows stratified sampling by the example population from figure 1.

Figure 1 Example population (deVries 1986)

Imagine the example population of \(N=30\) elements be subdivided into three strata as in figure 2. Here, stratification has been done arbitrarily into three strata of size 14, 8 and 8. From this stratified population, we wish to take a sample of \(n=10\), taking \(n_1=4\) from the first stratum and \(n_2=n_3=3\) from the other two strata. The stratum parametric means and variances are given in table 1.

Table 1 Stratum parameters for the stratified example population.

Figure 2 Subdividing the example population (arbitrarily) in three strata, for illustration purposes

Calculation in stratified sampling is best done in tabular format, first per stratum and then combining the per-stratum results to the values / estimations for the entire population. The estimation of the mean is illustrated in Table 2 and results – as expected – in the parametric mean without stratification. Table 3 presents the calculation of the parametric error variance for \(n=10\) and the defined allocation of samples to the three strata.

Table 2 Calculation of parametric population mean from the parametric strata means.

Table 3 Calculation of parametric error variance of the estimated mean of the population for \(n=10\).

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