Linear vs. Quadratic Calibration

[misty]

I'm using a PE Clarus 500, FID, programmable on-column injection for ASTM D6584 analysis of Free and Total Glycerin in B-100 (bio-fuel). The ASTM calls for a 0.999 or better r^2 value for a five point curve. I'm doing this with a linear fit; however, I have information from another user that is using quadratic fit to accomplish the 0.999 r^2.

Any advantages/disadvantages to quadratic fit? I'm fairly new to GC work and am personnally in favor of linear calibration because that is what I know and use. I'll appreciate any input.

Thank you.

[tom jupille]

Jupille's Rules of linearity*:

Rule 1. Nothing in nature is exactly linear

Rule 2. Almost everything in nature is approximately linear -- over a narrow enough range.

Combine those with the famous "Occam's Razor" (other things being equal, simpler is better), and you come to the conclusion that if you're getting a reasonable linear fit, there's no point to using a quadratic.

As an aside, r^2 is arguably not a good measure of fit for wide-range chromatography data because it is dominated by errors at the upper end of the range and relatively insensitive to errors at the lower end. However, since that's what the standard calls for, that's what you have to use.

* Hey, if Mikhail Tsvett could name chromatography after himself, I may as well try!

[DR]

r² is uaually >0.99 if using a quadratic or higher power fit. I think you could probably get r²>0.99 on a water wiggle using a quadratic fit (use linear unless otherwise specified by your method or you're using a non-linear detection method).

[tom jupille]

Actually, DR, that's a good point. In fact, with three calibration points, you can get r^2 = 1.00 on a quadratic fit!

[misty]

Thank you both very much! Greatly appreciated.



Anyone else like to add?

[JI2002]

For a set of data, Correlation Coefficient(r) doesn't change no matter what calibration technique you are using. This is because you can calculate r without a curve. What changes though is Coefficient of Determination (R^2), You can always get better R^2 when you add an extra term, like from linear fit to quadratic fit. This is why Radj is uesd for quadratic or higher fit. Personally I believe that R^2 instead of r should be used in the description of calibration although r^2 is equal to R^2 for linear regression. Another note, if quadratic curved is used, more than 5 data points should be required for the calibration.