Inclusion probability
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| − | |text=Please always remember that the [[population]] we take samples of, is not the biological population of trees. Sampling in forestry is based on the selection of sample points and not trees. Afterwards an observation is derived by including trees at which we take the measurements (normally this is not only one tree, but e.g. all trees on a plot). Nevertheless we need to know the inclusion probability of each tree to derive an unbiased estimate for the target variable. | + | |text=Please always remember that the [[population]] we take samples of, is not the biological population of trees. Sampling in forestry is based on the selection of sample points and not trees. Afterwards an observation is derived by including trees at which we take the measurements (normally this is not only one tree, but e.g. all trees on a plot). Nevertheless we need to know the inclusion probability of each tree to derive an unbiased estimate for the target variable. This probability is the inverse of the [[expansion factor]] that one has to apply if an estimate of the total is targeted. |
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Revision as of 16:26, 20 January 2011
In probabilistic sampling each element of the population must have a non-zero probability to be included in a sample, otherwise unbiased estimation is not possible. The inclusion probability \({\pi}_i\,\) refers to the chance that the \(i^{th}\) population element becomes part of a sample. The inclusion probability should be distinguished from the selection probability \(p(s)\) of a sample that is the probability that a certain unordered set of elements is selected as sample.
Inclusion zone concept
Sampling for forest attributes is in some aspects not directly comparable to basic statistical concepts we learn in school. Contrary to basic examples of probabilistic sampling, like the probabilities in a deck of cards or other finite populations, sampling for area related forest attributes take place in an infinite areal sampling frame. As the random selection of samples is based on the selection of dimensionless points in an area of interest, there is an infinite number of possibilities.
Important
- Please always remember that the population we take samples of, is not the biological population of trees. Sampling in forestry is based on the selection of sample points and not trees. Afterwards an observation is derived by including trees at which we take the measurements (normally this is not only one tree, but e.g. all trees on a plot). Nevertheless we need to know the inclusion probability of each tree to derive an unbiased estimate for the target variable. This probability is the inverse of the expansion factor that one has to apply if an estimate of the total is targeted.
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This section is still under construction! This article was last modified on 01/20/2011. If you have comments please use the Discussion page or contribute to the article! |
