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Problem using the Cubic Spline with a non-linear set of concentrations including a zero standard.

Document ID: DQ316
Relevant to following products: WorkOut 2.5 Manta 2.5
Document description: Problem using the Cubic Spline with a non-linear set of concentrations including a zero standard.



When using the Cubic Spline with a non-linear set of concentration standard values the Log/Anti-Log X setting is typically ticked (to account for the non-linear concentration values).

The following set of standards illustrates a typical set of concentration values where this problem might arise:

Standard1 0
Standard2 0.1
Standard3 0.39
Standard4 0.11
Standard5 5.1
Standard6 19

Here, the first standard's concentration is defined as 0. With this setting the standard point is not included in the Cubic Spline (because 0 cannot be logged). As a consequence of this Standard2 is the first defined standard used in the Cubic Spline and the values within the range of Standard1 and Standard2 will be calculated using interpolation.

To avoid this problem and ensure the 0 standard is included, some people specify the 0 standard's concentration value to use for the Spline as a very small value, such as 0.00000001. This ensures that the data point is included in the Spline with the Log/Anti-log. However, setting a very small value can cause the Cubic Spline to develop a turning point within the range of standards, making the curve useless for interpolation, e.g.


In these situations it is better to ensure the 0 standard value is defined as a small non-zero value, such as 0.01.



This ensures the Spline is used to calculate all values within the range of standards.






Related articles:
DQ010: My Cubic Spline has a kink in it
How To: Use Cubic Spline with non-linear data…

DQ023: Can I extrapolate with the Cubic Spline?
How to: Allow/disallow extrapolation with a Cubic Spline…

DQ024: Why are the MSE and SS of my Cubic Spline large?
How is the MSE and SS of Cubic Spline calculated?





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