A new proposal for a principal component-based test for high-dimensional data applied to the analysis of PhyloChip data

A modification of the principal component test is presented. It uses a weighted combination of the sums of squares for different principal components and is thus more powerful in high-dimensional settings with small sample sizes. Under usual normality assumptions, a rotation test is proposed which enables an exact conditional parametric test. The procedure is demonstrated with microarray data for the bacterial composition in the rhizosphere of different potato cultivars. In simulation studies, the power of the proposed statistic is compared with the competing multivariate parametric tests.