View source for Approaches to populations of sample plots

==Approach 1==

[[File:4.8-fig68.png|right|thumb|300px|'''Figure 1''' Illustration of    approach 1 for plot populations: subdivision of the forest area into    sample plots of identical shape and size, here: square and hexagonal    sample plots. Such a subdivision is also possible for rectangles and    some types of triangles (Kleinn and Vilcko 2005<ref   name="kleinn_vilcko2005">Kleinn  C. und F. Vilčko. 2005. Ein   Vergleich von zwei methodischen Konzepten  für die Grundgesamtheit von   Probeflächen bei Waldinventuren. AFJZ  176(4):68-74.</ref>).]]
[[File:4.8-fig69.png|right|thumb|300px|'''Figure   2''' An identical “forest area” subdivided in two different ways in   square sample plots of the same basic size. Right: plot fragments occur   along the border   line. The total of “number of stems” is obviously   identical in both cases; but this is not the case for the per-plot   parametric mean and variance (Kleinn and Vilcko 2005<ref   name="kleinn_vilcko2005">Kleinn  C. und F. Vilčko. 2005. Ein   Vergleich von zwei methodischen Konzepten  für die Grundgesamtheit von   Probeflächen bei Waldinventuren. AFJZ  176(4):68-74.</ref>).]]
[[File:4.8-fig70.png|right|thumb|300px|'''Figure   3''' Illustration of approaches for plot populations for the same   example population. Left: discrete population of square sample plots   with defined positions. Right: each point in the area is a sampling   element the value of which is determined by the surrounding trees   (sample plot). Each point has a value which is here indicated through   the cloud of points; in addition a trend surface is given (Kleinn and   Vilcko 2005<ref  name="kleinn_vilcko2005">Kleinn  C. und F.   Vilčko. 2005. Ein  Vergleich von zwei methodischen Konzepten  für die   Grundgesamtheit von  Probeflächen bei Waldinventuren. AFJZ    176(4):68-74.</ref>).]]
An intuitive approach is to imagine this population as the set of sample plots that covers the area of interest completely. This is depicted in Figure 1 for the two examples of square and hexagonal fixed area sample plots. The population consists of a discrete number of plots (see Figure 3, left). The sampling process is to select some of these plots. However, this approach does pose a series of interpretation and analysis problems; it works only for [[fixed area plots]] and within the class of fixed area plots only for some plot shapes. For the most frequently used circular plot, for example, this concept can not be applied.

Also, once the [[Forest Definition|forest]] area of interest is defined (the area sampling frame), it is not clearly defined as well how the plots come to lie. Figure 2 shows one and the same population over which two different grids of plots are overlaid. In one case the square plots fit perfectly into the square area [[population|sampling frame]], in the other case, there are various [[Fixed area plots at the stand boundary|border plots]] with smaller size. The per-plot mean and variance will be different between the two sub-divisions; this is certainly an undesirable property of a population concept that the population parameters are not clearly defined. We conclude that this simple concept of populations of sample plots is not well suited as a model for forest inventory sampling.