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Measure of fitness for calibration curves
Posted: Wed Sep 22, 2021 7:32 am
by sbashkyrtsev
After we built a curve, there are multiple ways to check how well it fits the data:
- R² - this one seems to be popular, but I've also heard complaints that it's not the best indicator
- Residuals - this one will highlight the trends of curving the data around the fitted line, but it's a visual inspection. How acceptable are visual inspections in the lab, and how acceptable are they for the regulators?
Are there other statistics that you'd recommend looking into?
Re: Measure of fitness for calibration curves
Posted: Wed Sep 22, 2021 8:28 am
by bunnahabhain
We use a very simple method: Back calculation of the data. If each measured data point fits it's nominal concentration by > x % (x is dependent of the intended use of the calibration), it is acceptable. If the percent deviation is too large, the standard is rejected (if it is clearly an outlier) or the curve is rejected.
Re: Measure of fitness for calibration curves
Posted: Wed Sep 22, 2021 3:37 pm
by Steve Reimer
I will point out that the US EPA drinking water methods for PFAS 537.1 and 533 both use residual criteria and don't include a criterion for coefficient of determination.
Re: Measure of fitness for calibration curves
Posted: Thu Sep 23, 2021 7:00 am
by bunnahabhain
So does the SANTE/12830/2020 pesticide guideline:
The suitability of the chosen function should be demonstrated. Preferably, this should be accomplished by a residual analysis using the residuals, rather than reporting the coefficient of correlation (r) or determination (R2). [...] The regression residuals should be presented in a residual plot. Visual inspection should be applied to decide if di are randomly distributed and hence linear calibration is demonstrated. If a trend is visible in the residuals, the calibration model is not suitable and an alternative approach must be used (e.g. alternative calibration function, different/split calibration range).
Re: Measure of fitness for calibration curves
Posted: Thu Sep 23, 2021 11:39 am
by sbashkyrtsev
Thanks! So residuals it is. I'm concerned though that this "visual inspection" is a bit subjective:
Visual inspection should be applied to decide if di are randomly distributed and hence linear calibration is demonstrated.
You can always say that the data seemed to be random and you didn't notice patterns. Calculating the SD of residuals is more objective:
If the percent deviation is too large, the standard is rejected (if it is clearly an outlier) or the curve is rejected.