Catlin-Groves, Christina L and Kirkhope, Claire L and Goodenough, Anne E and Stafford, Richard (2009). Use of confidence radii to visualise significant differences in principal components analysis: Application to mammal assemblages at locations with different disturbance

Multivariate statistical analysis is a powerful method of examining complex datasets, such as species assemblages, that does not suffer from the oversimplification prevalent in many univariate analyses. However, identifying whether datapoints on a multivariate plot are clustered is subjective, as there is no determination of significant differences between the points and no indication of the level of certainty of those points. The validity of drawing such conclusions may therefore be considered suspect. This paper describes a method of bootstrapping calculated principal components to estimate a confidence radius, similar to confidence intervals in univariate techniques. Plotting 3D scatterplots of the principal components, with the size of the spherical point representative of the level of confidence of the estimate, gives a clear and visual indication of significant difference between the points – where spheres overlap there is no significant difference. We apply the technique to mammal assemblages at sites in Epping Forest (Essex, UK) that differ in the level of disturbance present and find that differences between some sites that appear large using traditional principal components analysis are actually not significantly different at the 95% confidence level, while other sites do differ significantly.