Statistics

Physics

Data mining

Artificial intelligence

Multivariate statistics

Ordination

Permutation (music)

Acoustics

Principal component analysis

Significance testing

Statistical analysis

Mathematics

Computer science

Statistical significance

Dimensionality reduction

Statistical hypothesis testing

PeerJ

Principal Component Analysis (PCA) is one of the most broadly used statistical methods for the ordination and dimensionality-reduction of multivariate datasets across many scientific disciplines. Trivial PCs can be estimated from data sets without any correlational structure among the original variables, and traditional criteria for selecting non-trivial PC axes are difficult to implement, partially subjective or based on ad hoc thresholds. PCAtest is an R package that implements permutation-based statistical tests to evaluate the overall significance of a PCA, the significance of each PC axis, and of contributions of each observed variable to the significant axes. Based on simulation and empirical results, I encourage R users to routinely apply PCAtest to test the significance of their PCA before proceeding with the direct interpretation of PC axes and/or the utilization of PC scores in subsequent evolutionary and ecological analyses.

PCAtest: testing the statistical significance of Principal Component Analysis in R