Population

Population and sampling frame

A sampling study starts with a number of questions that refer to a certain domain of interest. That domain is called the population and is defined as the totality of all elements. The number of elements from which a sample should be drawn is called the sampling frame which is a list of all elements that can be selected during statistical sampling (all elements that have a selection probability larger than 0).

In the ideal case the sampling frame contains all elements of a population, however one can imagine reasons for differences of both. It is important to note that both, population and sampling frame, should be clearly defined for any sampling study. Reasons for a sample frame that is smaller as the population is for example, that parts of the population can not be sampled, because they are not accessable. In forest inventories we can imagine, that areas with extrem steep slopes can not be sampled. In those cases one should consider to re-define the population.

Note:

By means of a sampling study one is able to derive statistical sound estimations for the part of the population that is in the sample frame. If the pupolation is larger than the sample frame, we can not justify any estimations assigned to the whole population.

In forestry we are typically interested in estimating variables of forests or trees. Nevertheless the sampling frame is rarely the set of all trees in a forest area, but the area itself. This area consists of a infinit number of dimensionless points from which one selects a certain number as sample points. This definition is also called an area sampling frame. Around such a sample point we define a certain area that is the sample plot where the observation one makes on this area is assigned to the respective point.

Important!

The elements that are sampled and of which the sample frame consists are the sample plots and not single trees! In other words: one selects areas in the forest (and observe the trees on these plots) and not trees. This fact has far reaching consequences for the statistical issues.