by
Pear » Wed Oct 12, 2022 5:13 pm
James_Ball wrote:
So many try to stay away from quadratic fit, but often times it is the best fit, especially when you can see the points form a nice smooth curve instead of a straight line.
Using quadratic to "fix" a calibration that has scatter of points above and below the line over the calibration range is always bad. But often we see a nice bow in the points and that is where quadratic works best. The downside to quadratic is when any point falls outside of the range of the calibration. I have seen some curves that bow so much that once you get a little above the response of the upper point, your calculated results begin to decrease and if the response is high enough above the upper calibration point the result will even go negative. If an analyst is not paying attention to the overall size of the response and only the final value it can lead to a false report of not detected when is reality it is a very large result.
As for a DAD always being linear, as with all detectors they are linear over a certain range, but not for all ranges. If there is anything present that either enhances or reduces the response a tiny amount, then it will cause a deviation at low concentrations, and once saturation is reached, there are deviations at the high end of the range.
You also have to take into account everything happening to the analyte as it goes through the system. With my GCMS run that has over 150 analytes in it, I will have one analyte that gives less than 1% RSD on an average response factor calibration or near 1.0 r2 while another analyte will give 50% RSD and a 0.8r2 while the quadratic fit is 0.997. Same run and same conditions but each analyte responds to the complete system differently, and same can happen for LC and UV detectors. Beer's Law works in a perfect world, but just as in Physics lab, not all real life situation are in a vacuum on a frictionless surface.
Thanks so much for the reply James.
My calibration range 0.1 - 6ppm...so hardly huge so I thought I'd be fine. But 6 entirely independent calibration sets all show extremely high accuracy when set to quadratic. Approximately 101% accuracy at my two lowest calibration points, whereas linear is 110%~ at the same two points.
I wondered if this was due to the range, so I made 6 independent 6 point calibration sets from 0.1 - 2.5ppm. Accuracy is increased at the low end compared to the 6ppm calibration runs, but again, setting it to quadratic tightens up that low end accuracy so much more than linear.
The linear calibration example below (0.1-6ppm) doesn't scream quadratic as say an IC suppressed anion calibration curve does, but the data doesn't lie.
Curve as linearSame curve as quadraticBut 0.1-6ppm isn't exactly a range I'd expect a UV detector to deliver a non-linear data set?