it's common practice to perform principle component analysis (pca) on binned proton (¹h) spectra in nmr metabolomics, with each sample collected and processed in triplicate or higher to provide a statistical basis for its location in pca scores space. in the same way that the student's t statistic may be used to calculate confidence intervals on the real line, the hotelling T² statistic may be used in two dimensions or higher to determine confidence regions.

almost on a whim, i decided to write hotelling to calculate confidence ellipses for pca scores space data in two dimensions. it's written in highly portable and efficient ansi c, directly reads scores exported from SIMCA-P (the statistical package used in our group), and outputs ellipse data readable by gnuplot.

calculation of the parameters of the hotelling T² ellipses requires an eigendecomposition of the covariance matrix calculated from the individual scores space points. since the problem is constrained to two dimensions, the matrix's characteristic function is quadratic in form and the eigenvalues and eigenvectors may be calculated easily in closed form. hotelling then uses the parametric form of the ellipse equation to generate gnuplot-plottable ellipse contours such as these:

of course, this page would be useless without source code, huh? :P

• hotelling-src.tar.gz