Stratified sampling examples

Example 1

Illustration why stratification is most efficient when the strata means are as different as possible

Imagine the example population of \(N=30\) elements be subdivided into three strata as in the figure on the right. 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.

Stratum	\(N_h\,\)	\(n_h\,\)	\(\mu_h\,\)	\(\sigma_h^2\,\)
1	14	4	6.29	3.49
2	8	3	10.13	4.86
3	8	3	5.38	2.48

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