Modern analytical measurements are commonly presented in the form of vectors (e.g., spectra) or higher order data structures such as matrices, and these are often subjected to multivariate data analysis strategies to extract information. One aspect of these measurements that is often poorly understood is the underlying nature of the measurement errors and how these affect the ability to obtain chemical information. This Account outlines some of the methods that can be used to characterize multivariate measurement errors and how this information can be used to improve the results of data analysis. Characterization includes general classifications of error, Fourier domain representations, and the error covariance matrix. The calculation and interpretation of error covariance and correlation matrices are illustrated using experimental measurements, and data analysis methods that make use of this error information are briefly reviewed. A simple example is presented to show how information about measurement errors allows for more effective extraction of meaningful chemical variance in the data.
measurement errors; error covariance; Fourier transforms; multivariate data analysis; measurement noise
