Chemometrics in Spectroscopy Linearity in Calibration: Quantifying Nonlinearity, Part II

摘要

At this point in our series dealing with linearity, we have determined that the data under investigation do indeed show a statistically significant amount of nonlinearity, and we have developed a way of characterizing that nonlinearity. Our task now is to come up with a way to quantify the amount of nonlinearity, independent of the scale of either variable, and even independent of the data itself. In our last few columns (1-5), we devised a test for the amount of nonlinearity present in a set of comparative data (for example, as are created by any of the standard methods of calibration for spectroscopic analysis), and then pointed out a flaw in the method. The concept of a measure of nonlinearity that is independent of the units that the X and Y data have is a good one. The flaw is that the nonlinearity measurement depends upon the distribution of the data; uniformly distributed data will provide one value, normally distributed data will provide a different value, randomly distributed (i.e., what is found commonly in "real" data sets will give still a different value, and so forth, even if the underlying relationship between the pairs of values is the same in all cases.