Relations between Mid-Infrared and Near-Infrared Spectra Detected by Analysis of Variance of an Intervariable Data Matrix

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Abstract
A mathematical procedure based on the analysis of variance of an intervariable data matrix (AVID) was used to relate wavenumbers and wavelengths between the mid-infrared and near-infrared domains. Initially the method calculates for each sample the product of intensities at all combinations of the frequencies in the two domains. This data matrix is submitted to analysis of variance (ANOVA) based on a classification criterion. This procedure gives a matrix of Fisher F values for all possible combinations of wavenumbers and wavelengths. To remove the masking effect due to a few extremely significant frequencies and to highlight the relations between the frequencies, this matrix of F values was corrected by subtraction of a matrix of independence. The examination of the corrected data matrix allowed the assignment of the most important peaks for the discriminating criterion. This procedure also allows the study of vector profiles, where one spectral domain is examined in relation to a particular frequency in the other domain. The study of vector profiles is a very useful tool to see the relations between the wavenumbers and wavelengths of the two domains under study.