Spectral imaging in the scanning electron microscope (SEM) equipped with an energy-dispersive X-ray (EDX) analyzer has the potential to be a powerful tool for chemical phase identification, but the large data sets have, in the past, proved too large to efficiently analyze. In the present work, we describe the application of a new automated, unbiased, multivariate statistical analysis technique to very large X-ray spectral image data sets. The method, based in part on principal components analysis, returns physically accurate (all positive) component spectra and images in a few minutes on a standard personal computer. The efficacy of the technique for microanalysis is illustrated by the analysis of complex multi-phase materials, particulates, a diffusion couple, and a single-pixel-detection problem.