An improved method is provided for determining when a set of multivariate data (such as a chromatogram or a spectrum) is an outlier. The method involves using a procedure such as Principal Component Analysis to create a model describing a calibration set of spectra or chromatograms which is known to be normal, and to create residuals describing the portion of a particular spectrum or chromatogram which is not described by the model. The improvement comprises using an average residual spectrum calculated for the calibration set, rather than the origin of the model as a reference point for comparing a spectrum or chromatogram obtained from an unknown sample. The present invention also includes separating a complex set of data into various sub-parts such as sub-chromatograms or sub-spectra, so that outliers in any sub-part can be more readily detected. In one particular embodiment, the invention is directed towards a method for dividing a chromatogram into the sub-parts of peak information, baseline shape, baseline offset, and noise.