Analyses of a priori hypotheses about multivariate data may be summarized as a series of steps (modified from Anderson 2001):

1. Choose transformation and standardization (if any) to apply to the data
2. Choose appropriate distance measure
3. Conduct statistical tests
4. Visualize patterns of resemblance among observations

Similarly, classification of sample units into groups is a series of steps:

1. Choose transformation and standardization (if any) to apply to the data
2. Choose appropriate distance measure
3. Apply clustering or other algorithm to identify groups
4. Visualize patterns of resemblance among observations

Step 3 is the only one that differs between these two lists.  We’ve covered steps 1, 2, and 3 already.  Visualizing patterns (step 4) simply means illustrating what the statistical tests have identified or showing the groups that have been identified through a classification process.  This is one of the key purposes of ordination.  Visualization is common but optional; there is no statistical test associated with an ordination.

Another purpose of ordinating data is to reduce data dimensionality.  Ordinations seek to reduce the dimensionality of a dataset while minimizing the amount of information that is lost.  This is necessary to visualize patterns but can also be useful in other ways.  In some instances, for example, the reduced data themselves subjected to statistical analysis.

In this section, we will consider several types of ordination methods:

• Principal Component Analysis (PCA)
• Correspondence Analysis (CCA) and variants (DCA, CCA, DCCA)
• Non-metric MultiDimensional Scaling (NMDS),
• Principal Coordinates Analysis (PCoA; aka metric multidimensional scaling (MDS)),
• ReDundancy Analysis (RDA)
• Distance-based Redundancy Analysis (db-RDA; aka Canonical Analysis of Principal Coordinates (CAP))

After surveying a range of ordinations, we will compare ordination techniques, review general graphing principles, and focus on how to visualize and interpret ordinations.

References

Anderson, M.J. 2001. A new method for non-parametric multivariate analysis of variance. Austral Ecology 26:32-46.