A colleague sent the following to me at work today and after perusal of
various texts (Neter et al, Pedhazur, Cohen, etc.) I am unable to give
anything but an opinion.......here is what he sent:
"Can you answer me the following question. It concerns what is the
appropriate standard error (SE) from a curve fitting program when what one
wants to plot is derived from a COMBINATION of certain parameters, each of
which has its own SE, specifically,
I fit parabolas to some data, sensitivity (y) as a function of pupil
position (x)
y = ax^2 + bx + c
>From trivial Calculus, the peak of this function is at -b/2a
Now, I have seperate SEs for a, b and c from the fits.
What is the best SE to use for -b/2a ? For example, do the SEs add?"
At first he proposed an equation that took the square root of the variance
of the estimates, i.e., sqrt(SE^2 lin + SE^2 quad). My feeling was that
given the partialed nature of standard errors in a multiple regression
context, it may be misleading to add the respective standard errors, e.g.,
SE for the linear component + SE for the quadratic component, etc.,
especially given the collinearity (if centering not performed) of the terms.
However, I also understand that variance components can be additive. Anyway,
if anyone has a general opinion I would be most appreciative as I am a bit
stumped on this one...............thank you...........dale glaser
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