Pair difference technique example

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Forest Inventory lecturenotes

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Example 1

Systematic sampling from the example population in Figure 1 (Klein 2007).

Figure 1 Example population of 30 unequally sized strip plots; here, the ratio estimator may be apllied for estimation using plot size as covariable(de Vries 1986)

Taking a systematic sample of \(n=10\) elements, there are not many possibilities in our small example population. In fact, if the there shall be an equal distance between the elements in the list, this distance must be \(30/10=3\). Then, there are only three possible systematic samples having element 1, 2, or 3 as starting elements and then taking every third element. These three samples are listed and analyzed in Table 1.

Table 1 The population of all possible systematic samples of size \(n=10\) drawn from the example population. There are only 3 possibilities. PD-5 and 9 are the estimated error variances from the pair differences method with 5 non-overlapping and 9 overlapping pairs of sampled values.