I am performing an experiment where I'm measuring two variables, say $x$ and $y$, but I'm actually interested in a third variable which I calculate from those two, $$z=f(x,y).$$ In my experiment, of course, both $x$ and $y$ have experimental uncertainties, which are given by the resolution of my measurement apparatus among other considerations. I am also considering doing multiple runs of measurement to obtain good statistics on my measurement of $x$ and $y$, and therefore on $z$. I don't really know how the statistical spread will compare to my calculated (resolution-induced) uncertainty, though.
I would like to know what the final uncertainty for $z$ should be, and I am not very familiar with the error propagation procedures for this.
- What are the usual ways to combine the experimental uncertainties in measured quantities?
- When should I use the different approaches?
- How do I include statistical uncertainties when they are present?
- What happens if the statistical spread of a variable is comparable to the instrument's resolution, so that I can't neglect either contribution?
- What are good references where I can read further about this type of problem?
I would also appreciate answers to cite their sources - and particularly to use 'official' ones - where possible.