[scwilson]

Hello, my fellow chemical brethren (and sisters),

I was hoping to find some help with a derivation for the following formula:

$$\delta_c = S_r/m\sqrt{1/M+1/N+\frac {(\overline S_{unk} - \overline S_{std})^2}{m^2 S_{xx}}}$$

This formula can also be found here: http://en.wikipedia.org/wiki/Calibration_curve#Error_in_calibration_curve_results or in most analytical chem texts.

Naturally, S_r is the standard deviation about regression, m is the slope of the (external) calibration curve, M is the number of replicates used in measuring the average signal of the unknown, S_unk. N is the number of standards and S_std is the average signal of the standards measured. S_xx is the summed deviations squared in the x-values, which in this case would be the concentration of the standards.

And, for the last bit of context, this formula provides the uncertainty in an x-value derived from a calibration curve. In other words, it provides the uncertainty in the concentration of an unknown solution, which was measured against an external calibration curve. I apologize if my provided context was unnecessary--this is an analytical chem forum, after all--but I just wanted to make sure that we're all on the same page.

Could anyone direct me to a text or pub of some sort which reviews the derivation of this formula? I understand, very well, the qualitative underpinnings of this formula, but have yet to find a mathematical derivation. I've asked my PI and several related faculty at my uni; they've all seen the derivation, but can't seem to find the appropriate text. I'd greatly appreciate the help. I'm a grad student in AChem and fairly comfortable with my stats, so by all means, don't be afraid to just throw me in some sort of general direction. At this point, I'm completely stuck, so ANY help would be very much appreciated.

Sorry for the wall of text and thank you in advance for any insight. Great forum!

[blaisem]

Did you try the citations on the Wikipedia page? Reference 6 seems promising and cites two analytical textbooks that might give you what you're looking for.

Beyond that, I guess you get to wade through journal search engines or scifinder.