Principal Component Analysis - PCA

The relationship between samples (columns) in terms of their variables cannot normally be visualised because this would require a plot with as many axes as there are variables (rows). If your study only includes 3 variables this is possible, but is quite impossible given 4 or more variables or species. PCA is a technique that may summarise the relationship between the samples in a small number of axes that can be plotted. For such a summarisation to work, there must be some degree of correlation between the descriptive variables so that the effect of a number of these variables can be combined into a single axis. For good general introductions to PCA for non-mathematicians see Kent & Coker (1992) and Legendre & Legendre (1983).

From the ordination drop-down menu CAP offers a PCA undertaken on either the correlation or variance-covariance matrix between the descriptors (the variables in the rows). Once either PCA correlation or PCA covariance is selected a PCA on the working data set is undertaken.

Output from a PCA is presented under a number of tabbed components that can each be viewed by clicking on the tab. These are described in turn below:

Variance-PCA

Scores-PCA

Eigenvectors-PCA

Cross products

PCA plot

Principal Axis vs Variable Plot

Scree Plot

If you wish to test if samples in a PCA are outliers using the Mahalanobis distance see PCA -Cor -Outlier R or PCA -covar -Outlier R

If you wish to run a PCA using R see Run R code