Stratified sampling examples
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[[File:5.2.6-fig74.png|right|thumb|300px|Figure 1: Illustration why stratification is most efficient when the ''strata means'' are as different as possible]] | [[File:5.2.6-fig74.png|right|thumb|300px|Figure 1: Illustration why stratification is most efficient when the ''strata means'' are as different as possible]] | ||
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Imagine the example population of <math>N=30</math> elements be subdivided into three strata as in figure 1. 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 <math>n=10</math>, taking <math>n_1=4</math> from the first stratum and <math>n_2=n_3=3</math> from the other two strata. The stratum parametric means and variances are given in Table 1. | Imagine the example population of <math>N=30</math> elements be subdivided into three strata as in figure 1. 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 <math>n=10</math>, taking <math>n_1=4</math> from the first stratum and <math>n_2=n_3=3</math> from the other two strata. The stratum parametric means and variances are given in Table 1. | ||
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!''Stratum'' | !''Stratum'' | ||
!''Stratum mean'' | !''Stratum mean'' | ||
| − | !''Weight <math>W_h | + | !''Weight <math>(W_h)</math>'' |
| − | !''mean | + | !''mean*weight'' |
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| + | [[File:5.2.6-fig75.png|right|thumb|300px|Figure 2: Subdividing the example population (arbitrarily) in three strata, for illustration purposes]] | ||
{{Construction}} | {{Construction}} | ||
[[Category:Forest Inventory Examples]] | [[Category:Forest Inventory Examples]] | ||
Revision as of 19:49, 16 December 2010
Example 1
Imagine the example population of \(N=30\) elements be subdivided into three strata as in figure 1. 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
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.
Stratum Stratum mean Weight \((W_h)\) mean*weight 1 6.29 0.466667 2.9333 2 10.13 0.266667 2.7000 3 5.38 0.266667 1.4333 7.0667 
Figure 2: Subdividing the example population (arbitrarily) in three strata, for illustration purposes
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