Experimental Design and Data Analysis for Biologists

In the previous chapter, we were mainly interested in R-mode analyses that were based on associations between variables and scaled objects indirectly, although correspondence analysis scaled both objects and variables simultaneously. In this chapter, the primary focus is Q-mode analyses that directly scale objects based on similarities or dissimilarities between them. The techniques based on dissimilarities attempt to display the dissimilarities between objects graphically, with the distance between objects on the plot (inter-object distances) representing their relative dissimilarity. The scores for objects on the axes of these scaling plots can be used as variables in subsequent analyses so the techniques in this chapter are also methods for variable reduction. Remember that objects represent sampling or experimental units, such as plots, organisms, aquaria, sites, etc.

Some of the dissimilarity measures for dichotomous and continuous variables were outlined in Chapter 15 (and see Legendre & Legendre 1998 for a much more complete treatment) and all of those dissimilarities can be used with the analyses in this chapter. However, the choice of dissimilarities is a crucial one and different dissimilarities can result in very different patterns in, and interpretations of, the analyses we will describe. Additionally, the form of transformation and/or standardization of variables and/or objects, combined with the dissimilarity measure, can also be very influential.