Univariate statistics refers to the set of tests and analyses used to analyse response variables in which every observation is expressed by a single value. Conversely, multivariate statistics is used to analyse response variables in which every observation consists in a set of values.
Here is a collection of links I found useful to navigate the jungle of multivariate statistics:
- http://cc.oulu.fi/~jarioksa/old_index.html and http://vegan.r-forge.r-project.org/ contains plenty of information on Jari Oknasen’s vegan, a very comprehensive R package for performing multivariate statistics.
- Jari Oknasen’s introduction to multivariate statistics in R (more by him on ordinations here)
- Pedro Martinez Arbizu’s package and function for post-hoc comparisons of perMANOVA models in R
- Full course “Recent Advances in Analysis of Multivariate Ecological Data: Theory and Practice” by P. Legendre and D. Borcard with video-recorded lectures and teaching material.
- https://stat.ethz.ch/pipermail/r-sig-ecology/2013-April/003736.html and http://r-sig-ecology.471788.n2.nabble.com/CCA-vs-NMDS-and-ordisurf-td7578060.html: interesting questions and answers about CCA, NMDS and ordisurf.
- http://ucfagls.wordpress.com/2011/06/10/what-is-ordisurf-doing/: Gavin Simpson sheds some light on the ordisurf() function, which uses Generalized Additive Models to assess the correlation between the result of an ordination and an environmental gradient of interest. Somehow complementary to a Mantel test, it allows to test for significant non-linear correlations between the result of an ordination (usually based on community composition data) and an environmental continuous explanatory variable.
- http://onlinelibrary.wiley.com/doi/10.1111/2041-210x.12018/abstract: “Dismantling the Mantel test” by Guillot and Rousset.