Ratio estimator sampling examples

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Forest Inventory lecturenotes

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Example 1:

Figure 1 Example of a population of 30 unequally sized strip plots; here, the ratio estimator may be applied for estimation using plot size as co-variable (DeVries 1986).

Recall \(k\)-tree sampling as presented and discussed in distance based plots. One approximation to estimation is to imagine a virtual circle plot through the \(k^{th}\) tree, that is, a circle which has a radius that corresponds to the distance between the sample point and the \(k^{th}\) tree. Depending on the distance to the kth tree, these circle plots will have very different sizes: in parts of the forest with a high stem density, the plots will be small and in low density sectors, the plots will be large.

It is some times suggested to use the ratio estimator to cope for this unequal plot sizes, just as we suggested it for the above case of unequally sized strip plots (Figure 1).

However, why is this not a good idea?

Recall what we said about the situations in which the ratio estimator is efficient: a high positive correlation between target variable and ancillary variable needs to be present. In our case, number of stems could be a target variable and plot size the ancillary variable. It can directly be seen without any calculations that the correlation is zero: the number of stems is constant \((k)\) and thus completely uncorrelated with plot area – it is always the same.

Therefore, application of the ratio estimator to improve precision of the empirical \(k\)-tree sampling estimators is useless.

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