Hi
We know that the sensitivity of a calibration curve would equal to the slope of the linear fitting of the data. What if the fitting is nonlinear? E.g. polynomial!
Any ideas?
The sensitivity of a nonlinear calibration curve refers to the rate of change of the response variable (i.e. the output) with respect to the predictor variable (i.e. the input). It is usually represented as the slope of the curve at a given point and is a measure of how sensitive the response is to changes in the predictor variable. A steep slope indicates high sensitivity, while a shallow slope indicates low sensitivity.
If the calibration curve is nonlinear, the sensitivity of the curve cannot be determined by simply calculating the slope of the linear fitting of the data. Instead, other methods must be used to calculate the sensitivity of the curve.
One approach is to use the concept of the derivative, which is a measure of the rate of change of a function at a specific point. The sensitivity of a nonlinear calibration curve can be approximated by the derivative of the curve at a specific point. This can be calculated using numerical differentiation methods such as finite differences or analytical methods, if the equation of the curve is known.
Another approach is to use the concept of the sensitivity coefficient, which is a measure of how much the output of a calibration curve changes with respect to a change in the input. The sensitivity coefficient can be calculated by dividing the change in the output by the change in the input. This can be done for different input values to generate a sensitivity map or profile.
In some cases, the non-linear calibration curve can be transformed to linear one by applying a mathematical transformation to the data (e.g. logarithmic, reciprocal) then the slope of the new linear curve can be considered as the sensitivity.
In conclusion, when the calibration curve is nonlinear, the slope of the linear fitting of the data is not enough to determine the sensitivity. More advanced methods need to be used such as, derivative, sensitivity coefficient or mathematical transformation.
Thanks Jobair. This makes a lot of sense . Do you have some references for this?
- Badges
- Science topic
- Similar topics
- Phytochemistry
- Extracts