Integration for Idiots, Part V: What Wolfram Meant
In Part IV, we worked toward a result that surprised many. The presence of an unexpected peak with an unremarkable value can have significant effects on the computed values of our peaks of interest.
Let's go over what we've learned.
First, that with a single peak we can pretty easily mark the left and right integration marks, and handle a sloping background. For these purposes, peaks that are so far apart they are not visible are single peaks. There were a couple in our examples over at 1600 seconds, but they don't matter.
Second, when peaks get close enough together to interfere, things become very complicated, and all sorts of significant errors can be introduced. The kinds of interference that can occur include:
- Interference between two clearly distinguishable peaks.
- Invisible interference in a pure, undetected co-elute at the same time as a peak of interest.
- Confusing interference causes by an unexpected, undetected peak between close peaks of interests.
Now let us turn to some slides from Dr. Meier-Augenstein's presentation at the hearing, which hasn't received much attention since it was released last Friday. It is all very relevant, but we'd like to highlight some very important points that may not have been sufficiently clear during the hearing, having gotten lost among other issues. (Transcript beginning on PDF page 1137 or so).
This points out the fundamental premise: that you know what you are looking at is a single compound of interest. We've seen in our examples above the various kinds of interference that can result if there are things you do not expect in the vicinity of the peak you are trying to measure - either contained in the peak, or close enough to overlap.
We've also shown in our examples above what happens when peaks overlap, and if minor peaks are contained in the peak of interest. We will end up asking questions about what LNDD has assumed, or perhaps presumed, or maybe even deemed to be the invariants of their methodology, and whether they are in fact, true.
But, let us turn our attention to the key point:
In the presence of overlapping peaks, the software, even the automatic software on the IsoPrime 2, cannot do computation that leads to correct results. If peaks of known substances overlap, the results will be wrong. If there are hidden peaks of unknown substances, the results will be wrong.
Basically, if the chemical and chromatographic separation isn't good, your results aren't good either. You can't do anything after the fact with your collected data to correct it.
Let's be completely clear about the relevance of this observation to the alternate B samples and the Stage 17 data reprocessed on the IsoPrime 2. If the conditions of chemical and chromatographic separation lead to consistently overlapped data sets, consistent results from automatic methods can still be incorrect. Consistency just means it repeatedly made the same unresolvable decisions.
After a few examples, the Doctor addresses an alternate formulation of the same problem in slide 16:
Once there are overlaps, of either known or unknowns, the results are not reliable. It's possible the software will pick the similar points and get consistent numbers, or that manual processing will allow you to get values in an "expected" range, but you won't know the truth.
With this background, we encourage you to look, perhaps for the first time, at Meier-Augenstein's presentation. Then, re-read his testimony beginning on PDF page 1131, and see if it doesn't make much more sense.
This concludes Integration for Idiots.
Our next series will be, "Idiots look at the Data". Based on our newfound understanding, do the data we see produced in the Landis case seem good enough to lead to reliable results? Are there unfounded and untested assumptions built into the collection conditions and the data set?
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