This might appear to be a trivial question, but my statistics skills are weak... Can someone explain to me how to calculate the error on the background measurement *below the peak* when we measure MULTIPLE backgrounds on each side and apply an exponential interpolation? My thoughts are that we should be able to calculate an error envelope around the exponential regression, and that the error on the background under the peak should be much lower than the individual errors on each background. Unfortunately I have no idea how such an error envelope is calculated (some program can do it, e.g. with isoplot, but when I tried, it bugs as the probability of fitting ends up to be close to zero)...
Since we are dealing with an exponential regression, I would guess a first step would be to change the exponential relation to a more easy to handle linear relation: if y = f(x) = a * exp (b * x) with y = counts and x = spectrometer position, then we can also write LN (y) = LN (a) + b * x - which is a "simple" linear equation.
Does this sounds correct?
But then... assuming the error on x is negligible (accurate spectrometer positioning) and having an error on the points that define the y = f(x) equation, how to calculate the error at a specific x position?
Maybe, to start the discussion, someone should remind me on the "simple" process how the background error is calculated on TWO points with an exponential curvature? Should we simply assume errors adds up in quadrature, i.e., bkg error = ( bkg_1 ^ 2 + bkg_2 ^ 2 + … + bkg_n ^ 2 ) / n??
Best, and thanks in advance for your help!
Dr. Julien Allaz
Electron microprobe manager
University of Colorado Boulder
Dept. of Geological Sciences
2200 Colorado Av.
Boulder, CO 80309-0399
Phone: (303) 735 2413
Lab: (303) 492 5251
Fax: (303) 492 2606
Visit my website! http://geoloweb.ch