4.3 Statistical Methods
71
Two trends can be noticed. On the one hand, there are tests suggested from a
mathematical point of view (Weiss 1960; Bickel 1969; Friedman & Rafsky 1979;
Henze 1988), which have not found many applications yet. On the other hand,
there are test procedures, which are applied for example in biology (e.g. Smith et
al. 1990; Clarke 1993; Schleier & van Bernem 1996), without precise knowledge
of their mathematical properties. In textbooks on the subject (e.g. Blining &
Trenkler 1994; Bortz et al. 1990) these tests are not mentioned. Thus, further research is required on this topic.
4.3.3.1
Non-Parametric Multivariate Tests
All the multivariate tests mentioned above follow the principle of randomization,
which has already been referred to in Sect. 4.2. As they are based on the pairwise
dissimilarities of the sampled objects, their application is strongly connected with a
decision about standardization and transformation of the data and with the choice
of a measure of dissimilarity. A discussion on this topic is found e.g. in Clarke
(1993), Kaufmann & Rousseeuw (1990), Ludwig & Reynolds (1988), Schleier &
van Bernem (1996) and Sokal & Rohlf (1981).
To graphically illustrate a result found with the help of non-parametric multivariate tests, MDS (compare Sect. 4.3.1.3) may be used, as it is also related to the
pairwise dissimilarities of objects.
4.3.3.2
Case Study: Communities After Experimental Defaunation
Data provided by A. Tecklenborg (compare Chap. 6).
Question: Are there differences between the communities on the control and on
the experimental sites?
Sampling: Five replicates were taken per sampling day from the control and
from each of the experimental sites.
Statistical technique: Calculation of the pairwise dissimilarities between all
pairs of replicates, Minimum Spanning Tree Test, graphical representation by
MDS.
Results: After the experimental defaunation, no individuals were left on the experimental sites, while on the control sites the number of individuals was "normal". In this case, a test is not necessary.
On 07.07.94, i.e. 21 days after colonization commenced, there were still clearly
less species and individuals on the experimental than on the control sites (Table 4.3.1).
The Minimum Spanning Tree (Schleier & van Bernem 1996) calculated with
Chord-distance is not unique. A number of 100 Minimum Spanning Trees was
calculated, which gave II subtrees on average. Under the null hypothesis of all
replicates coming from the same sampling universe, 16 subtrees are expected (pvalue 0.028). That means replicates from the experimental and from the control
sites represent two fairly strictly separated groups. Thus, the communities still
differ at that time.
71
Two trends can be noticed. On the one hand, there are tests suggested from a
mathematical point of view (Weiss 1960; Bickel 1969; Friedman & Rafsky 1979;
Henze 1988), which have not found many applications yet. On the other hand,
there are test procedures, which are applied for example in biology (e.g. Smith et
al. 1990; Clarke 1993; Schleier & van Bernem 1996), without precise knowledge
of their mathematical properties. In textbooks on the subject (e.g. Blining &
Trenkler 1994; Bortz et al. 1990) these tests are not mentioned. Thus, further research is required on this topic.
4.3.3.1
Non-Parametric Multivariate Tests
All the multivariate tests mentioned above follow the principle of randomization,
which has already been referred to in Sect. 4.2. As they are based on the pairwise
dissimilarities of the sampled objects, their application is strongly connected with a
decision about standardization and transformation of the data and with the choice
of a measure of dissimilarity. A discussion on this topic is found e.g. in Clarke
(1993), Kaufmann & Rousseeuw (1990), Ludwig & Reynolds (1988), Schleier &
van Bernem (1996) and Sokal & Rohlf (1981).
To graphically illustrate a result found with the help of non-parametric multivariate tests, MDS (compare Sect. 4.3.1.3) may be used, as it is also related to the
pairwise dissimilarities of objects.
4.3.3.2
Case Study: Communities After Experimental Defaunation
Data provided by A. Tecklenborg (compare Chap. 6).
Question: Are there differences between the communities on the control and on
the experimental sites?
Sampling: Five replicates were taken per sampling day from the control and
from each of the experimental sites.
Statistical technique: Calculation of the pairwise dissimilarities between all
pairs of replicates, Minimum Spanning Tree Test, graphical representation by
MDS.
Results: After the experimental defaunation, no individuals were left on the experimental sites, while on the control sites the number of individuals was "normal". In this case, a test is not necessary.
On 07.07.94, i.e. 21 days after colonization commenced, there were still clearly
less species and individuals on the experimental than on the control sites (Table 4.3.1).
The Minimum Spanning Tree (Schleier & van Bernem 1996) calculated with
Chord-distance is not unique. A number of 100 Minimum Spanning Trees was
calculated, which gave II subtrees on average. Under the null hypothesis of all
replicates coming from the same sampling universe, 16 subtrees are expected (pvalue 0.028). That means replicates from the experimental and from the control
sites represent two fairly strictly separated groups. Thus, the communities still
differ at that time.