4.3 StatistIcal Methods
59
4 "~--'-----'-----'-----~
D
or
3
~ 2
fil
'"
o
o ~----~----~----~----~
0.80
0.85
0.90
Data
0.95
1.00
Fig. 4.3.3 Shepard diagram of the distances in the MDS configuration of Fig. 4.3.2
For the data from the total sediment fraction (Fig. 4.3.2) the picture is different
(stress=0.07).
Ti0 2 is placed far away from all the others. From the corresponding Shepard
diagram (Fig. 4.3.3) one can see that the reason is not negative correlation. The
axis "Data" shows that all the calculated rank correlations are high or very high
(between 0.84 and 0.99). The interpretation of the MDS plot in this case is the
following: All of the variables are highly correlated. i.e. show a nearly identical
pattern.
4.3.1.5
Variability in Distribution Patterns
Question: Assessment of the background noise in the number of individuals of
macrozoobenthic species with the objective to describe a "reference situation" in
order to recognize changes caused by hydrography.
In the univariate case the background noise in the values is identified with their
variance. There is a high number of statistical parameters to characterize variability (see e.g. Lozan 1992; Sokal & Rohlf 1981), whose application is dependent
upon the question and the scale of the data. A "reference situation" may be described by an interval around a location parameter (in general mean or median).
The interval is chosen in such a way that values outside the interval will be fairly
rare. Such an interval can be represented graphically for example as a "Box-andWhisker-Plot" (median and quartiles) or as a "variance-interval" around the mean
(arithmetic mean and double standard deviation). Values inside the interval can be
termed "within normal fluctuation". the interval marks the variability of the empirical distribution. In a similar way a graphical test can be carried out. In this
case, the length of the interval must be equal to the confidence region of the respective parameter. Thus. the notches in "notched box plots" mark the 95 % confidence interval for the median, and an interval of the length of four times the stand-
59
4 "~--'-----'-----'-----~
D
or
3
~ 2
fil
'"
o
o ~----~----~----~----~
0.80
0.85
0.90
Data
0.95
1.00
Fig. 4.3.3 Shepard diagram of the distances in the MDS configuration of Fig. 4.3.2
For the data from the total sediment fraction (Fig. 4.3.2) the picture is different
(stress=0.07).
Ti0 2 is placed far away from all the others. From the corresponding Shepard
diagram (Fig. 4.3.3) one can see that the reason is not negative correlation. The
axis "Data" shows that all the calculated rank correlations are high or very high
(between 0.84 and 0.99). The interpretation of the MDS plot in this case is the
following: All of the variables are highly correlated. i.e. show a nearly identical
pattern.
4.3.1.5
Variability in Distribution Patterns
Question: Assessment of the background noise in the number of individuals of
macrozoobenthic species with the objective to describe a "reference situation" in
order to recognize changes caused by hydrography.
In the univariate case the background noise in the values is identified with their
variance. There is a high number of statistical parameters to characterize variability (see e.g. Lozan 1992; Sokal & Rohlf 1981), whose application is dependent
upon the question and the scale of the data. A "reference situation" may be described by an interval around a location parameter (in general mean or median).
The interval is chosen in such a way that values outside the interval will be fairly
rare. Such an interval can be represented graphically for example as a "Box-andWhisker-Plot" (median and quartiles) or as a "variance-interval" around the mean
(arithmetic mean and double standard deviation). Values inside the interval can be
termed "within normal fluctuation". the interval marks the variability of the empirical distribution. In a similar way a graphical test can be carried out. In this
case, the length of the interval must be equal to the confidence region of the respective parameter. Thus. the notches in "notched box plots" mark the 95 % confidence interval for the median, and an interval of the length of four times the stand-