Classical Least Squares, Part IX: Spectral Results from a Second Laboratory

May 01, 2012

This column is the next continuation of our discussion of the classical least squares (CLS) approach to calibration (1–8). In our previous column (8), we had found that neither weight percent, mole percent of the components, nor calculation of the percentage of hydrogen atoms from the various components, even after being corrected for density, gave results corresponding to the spectral results obtained.

Matters stood thus and this "mystery" was reported at Pittcon 2009 (9).

Table I: Experimental conditions used by the second laboratory
The report of these results generated considerable interest during that conference session. Comments from the audience ranged from "That's the simplest possible chemometric experiment, that's why nobody ever did it before!" to "It really should have worked!" and "I'm going to swear off chemometrics!" As we will see, however, matters were not so dire, although it did take some time and more work to unravel the "mystery." The results of that work, however, potentially point the way toward methods for improving the chemometric calibrations we develop.

At the end of the session, there was a small group of attendees that assembled to discuss possible ways to attack and solve this mystery. A consensus quickly developed that the first activity that good science calls for, especially when there's a mystery, is to repeat the experiment, and preferably to have a different scientist perform the repetition. David Heaps, at that time affiliated with AstraZeneca Corp., along with his colleague Kelly Sill-Drahos volunteered to repeat the experiment in his laboratory to verify that the results we had obtained were not spurious. The conditions used for this experiment are shown in Table I (compare with Table II of reference 5).

Besides the differences in equipment, there were some other minor differences between the two experiments. Some of the differences were purposeful and some were accidental. The following differences were known and predetermined:

  • Measurements were performed using both a 2-mm pathlength sample cell and a 1-mm sample cell.
  • Samples were made up by volume percent rather than weight percent.

An interesting dichotomy can be seen here. The first set of samples, made up according to the experimental design specified (see Table I in reference 5) used samples measured out to the weight values specified in the original experiment. In this second set of samples, the liquids were measured volumetrically using pipettes. Thus, because of the differences in densities between the various materials and the difference in interpretation of the design table, the mixtures used by the two laboratories were not the same, despite both of them adhering to the same experimental design.