From the histograms, do many variables seem normally distributed?
Note that normality is not required for explanatory variables in regression
analysis and in canonical ordination.
Do many scatter plots show linear or at least monotonic relationships?
Simple transformations, such as the log transformation, can be used to improve
the distributions of some variables (make them more symmetrical and closer to
normal distributions). Furthermore, because environmental variables are dimensionally heterogeneous (expressed in different units and scales), many statistical analyses
require their standardization to zero mean and unit variance. These centred and
scaled variables are called z-scores. We can now illustrate transformations and
standardization with our example data (Fig. 2.10).
dfs
200 600
0 20 50
40 70 100
0 2 4 6
4
8 1 2
0
200
200 600
ele
slo
0 20 40
0 30 60
dis
pH
7.8 8.2 8.6
40 70 100
har
pho
0 2 4
0 2 4 6
nit
amm
0.0 1.0
4
8 1 2
oxy
0 200 400
0 20 40
7.8 8.2 8.6
0
2
4
0.0 1.0
5 10
5
10
bod
Bivariate Plots with Histograms and Smooth Curves
Fig. 2.9 Scatter plots between all pairs of environmental variables with LOWESS smoothers
32
2 Exploratory Data Analysis