Finding that the experiments performed in two different laboratories gave substantially the same results, we redoubled our
efforts to determine the cause of the discrepancy between the spectral and reference concentrations. Serendipity leads to
This column is the last installment of our discussion of the classical least squares (CLS) approach to calibration (1–10).
Our previous column (10) discussed how we obtained results from the second laboratory that had essentially the same properties
as the results from the first laboratory, despite the fact that it was a different laboratory, the experiments were performed
by different scientists, and the mixtures used contained different materials. In both cases we examined the results for possible
experimental blunders, and for both laboratories we rejected the hypothesis that experimental problems were the cause of the
This being the case, we are forced to the conclusion that there is some real, previously unsuspected, physical phenomenon
affecting the behavior of the samples or the spectroscopic measurement. At this point, we have no clue as to the nature of
the phenomenon. The only course of action left to us is to continue the analysis of the data as we had done previously, keeping
an eye out for any other unexpected effects that might relate to an explanation of the results. The next step in the analysis
of the first set of experimental measurements was to compute the mole percent values of the various mixture components, and
compare those values with the CLS values computed from the spectral data. Therefore, we computed the mole percents for the
samples from the second laboratory, and compared them with the spectral results. Table I presents that set of comparisons.
Table I: Comparisons of spectroscopic values with mole percents for data from the second laboratory
We can see that the agreement between the CLS-determined percents and the mole percents is about the same as what we found
in the comparison with weight percents, with errors for some samples being as much as 10–15%.
Furthermore, from Table IV in part X of this series (10) (for weight percents from the second laboratory) as well as from
Table V in part VIII (8) (for mole percents from the first laboratory), we find that the nature and the approximate magnitudes
of the discrepancies are roughly the same for all three sets of comparisons.
This finding was both encouraging and discouraging. It was encouraging because it demonstrated whatever the effects that are
operative, they are reproducible, and this provides further confirmation that they represent real physical phenomena, even
though we didn't know which phenomena those were. On the flip side of the coin, it was discouraging for the same reason: It
provided no further insight into the nature of the cause (or causes) of the errors.
At this point, there seemed to be no further direction to go in other than to continue the analysis of the data the same way
we did according to the previous schema: to compute the percentage of hydrogen atoms from each component of the mixtures,
and then compute the percentage of hydrogen atoms after correcting for the density of the various components. It was all a
bit depressing, since there was no real expectation that we would find some new or different results that would point us in
the proper direction.