LAUSR

Abstract The traditional use of p values both for univariate distributions and for Design of Experiments is described. In chemometrics they may additionally be calculated to provide an estimate of the significance of variables in non-orthogonal experimental matrices, for example as potential markers in a metabolomic analysis. The difficulties of interpreting these non-orthogonal variables is discussed. A set of simulations, each consisting of four variables, two variables which have varying levels of correlation, is described. As the correlation reduces between these two variables, so their calculated p values become smaller. An incorrect conclusion about the significance of individual variables may be obtained if there is a high correlation between them, although this depends on the intensity, relative to noise, of the variables of interest. The paper provides a numerical illustration of how serious this distortion is.